Mixing
Solve this differential equation dy/dx [closed]
$begingroup$
Solve this differential equation where
ordinary-differential-equations differential
edited Feb 2 at 4:22
Robert Lewis
48.9k23168
asked Feb 2 at 3:42
Udit Anjali SwaroopaUdit Anjali Swaroopa
41
$endgroup$
closed as off-topic by Claude Leibovici, Mark Viola, Decaf-Math, Dave, Cesareo Feb 2 at 7:55
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Claude Leibovici, Mark Viola, Decaf-Math, Dave, Cesareo
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
Solve this differential equation where
ordinary-differential-equations differential
edited Feb 2 at 4:22
Robert Lewis
48.9k23168
asked Feb 2 at 3:42
Udit Anjali SwaroopaUdit Anjali Swaroopa
41
$endgroup$
closed as off-topic by Claude Leibovici, Mark Viola, Decaf-Math, Dave, Cesareo Feb 2 at 7:55
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Claude Leibovici, Mark Viola, Decaf-Math, Dave, Cesareo
If this question can be reworded to fit the rules in the help center, please edit the question.
$begingroup$
Is that a demand? If so, then no; you solve it.
$endgroup$
– Mark Viola
Feb 2 at 3:51
$begingroup$
This is quite straightforward to solve. Show us you've put some effort into it and we'll help you where you got stuck.
$endgroup$
– Rhys Hughes
Feb 2 at 3:57
1
$begingroup$
Your question is headed for closure, since (1) you didn't write out the equation in $LaTeX$, which is inconvenient for your readers; (2) you didn't provide any context--information about why this is a problem of interest, or what you have tried. Not to worry, it takes a while to get the hang of the culture around here. Anyway, I've tried to give you a pointer in my answer below. Welcome to MSE, and Cheers!
$endgroup$
– Robert Lewis
Feb 2 at 4:00
$begingroup$
I also added the "differential-equations" tag to your post.
$endgroup$
– Robert Lewis
Feb 2 at 4:23
add a comment |
$begingroup$
Solve this differential equation where
ordinary-differential-equations differential
edited Feb 2 at 4:22
Robert Lewis
48.9k23168
asked Feb 2 at 3:42
Udit Anjali SwaroopaUdit Anjali Swaroopa
41
$endgroup$
Solve this differential equation where
ordinary-differential-equations differential
ordinary-differential-equations differential
edited Feb 2 at 4:22
Robert Lewis
48.9k23168
asked Feb 2 at 3:42
Udit Anjali SwaroopaUdit Anjali Swaroopa
41
edited Feb 2 at 4:22
Robert Lewis
48.9k23168
asked Feb 2 at 3:42
Udit Anjali SwaroopaUdit Anjali Swaroopa
41
edited Feb 2 at 4:22
Robert Lewis
48.9k23168
edited Feb 2 at 4:22
Robert Lewis
48.9k23168
edited Feb 2 at 4:22
Robert Lewis
48.9k23168
48.9k23168
asked Feb 2 at 3:42
Udit Anjali SwaroopaUdit Anjali Swaroopa
41
asked Feb 2 at 3:42
Udit Anjali SwaroopaUdit Anjali Swaroopa
41
asked Feb 2 at 3:42
Udit Anjali SwaroopaUdit Anjali Swaroopa
41
41
closed as off-topic by Claude Leibovici, Mark Viola, Decaf-Math, Dave, Cesareo Feb 2 at 7:55
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Claude Leibovici, Mark Viola, Decaf-Math, Dave, Cesareo
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Claude Leibovici, Mark Viola, Decaf-Math, Dave, Cesareo Feb 2 at 7:55
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Claude Leibovici, Mark Viola, Decaf-Math, Dave, Cesareo
If this question can be reworded to fit the rules in the help center, please edit the question.
$begingroup$
Is that a demand? If so, then no; you solve it.
$endgroup$
– Mark Viola
Feb 2 at 3:51
$begingroup$
This is quite straightforward to solve. Show us you've put some effort into it and we'll help you where you got stuck.
$endgroup$
– Rhys Hughes
Feb 2 at 3:57
1
$begingroup$
Your question is headed for closure, since (1) you didn't write out the equation in $LaTeX$, which is inconvenient for your readers; (2) you didn't provide any context--information about why this is a problem of interest, or what you have tried. Not to worry, it takes a while to get the hang of the culture around here. Anyway, I've tried to give you a pointer in my answer below. Welcome to MSE, and Cheers!
$endgroup$
– Robert Lewis
Feb 2 at 4:00
$begingroup$
I also added the "differential-equations" tag to your post.
$endgroup$
– Robert Lewis
Feb 2 at 4:23
add a comment |
$begingroup$
Is that a demand? If so, then no; you solve it.
$endgroup$
– Mark Viola
Feb 2 at 3:51
$begingroup$
This is quite straightforward to solve. Show us you've put some effort into it and we'll help you where you got stuck.
$endgroup$
– Rhys Hughes
Feb 2 at 3:57
1
$begingroup$
Your question is headed for closure, since (1) you didn't write out the equation in $LaTeX$, which is inconvenient for your readers; (2) you didn't provide any context--information about why this is a problem of interest, or what you have tried. Not to worry, it takes a while to get the hang of the culture around here. Anyway, I've tried to give you a pointer in my answer below. Welcome to MSE, and Cheers!
$endgroup$
– Robert Lewis
Feb 2 at 4:00
$begingroup$
I also added the "differential-equations" tag to your post.
$endgroup$
– Robert Lewis
Feb 2 at 4:23
$begingroup$
Is that a demand? If so, then no; you solve it.
$endgroup$
– Mark Viola
Feb 2 at 3:51
$begingroup$
Is that a demand? If so, then no; you solve it.
$endgroup$
– Mark Viola
Feb 2 at 3:51
$begingroup$
This is quite straightforward to solve. Show us you've put some effort into it and we'll help you where you got stuck.
$endgroup$
– Rhys Hughes
Feb 2 at 3:57
$begingroup$
This is quite straightforward to solve. Show us you've put some effort into it and we'll help you where you got stuck.
$endgroup$
– Rhys Hughes
Feb 2 at 3:57
1
1
$begingroup$
Your question is headed for closure, since (1) you didn't write out the equation in $LaTeX$, which is inconvenient for your readers; (2) you didn't provide any context--information about why this is a problem of interest, or what you have tried. Not to worry, it takes a while to get the hang of the culture around here. Anyway, I've tried to give you a pointer in my answer below. Welcome to MSE, and Cheers!
$endgroup$
– Robert Lewis
Feb 2 at 4:00
$begingroup$
Your question is headed for closure, since (1) you didn't write out the equation in $LaTeX$, which is inconvenient for your readers; (2) you didn't provide any context--information about why this is a problem of interest, or what you have tried. Not to worry, it takes a while to get the hang of the culture around here. Anyway, I've tried to give you a pointer in my answer below. Welcome to MSE, and Cheers!
$endgroup$
– Robert Lewis
Feb 2 at 4:00
$begingroup$
I also added the "differential-equations" tag to your post.
$endgroup$
– Robert Lewis
Feb 2 at 4:23
$begingroup$
I also added the "differential-equations" tag to your post.
$endgroup$
– Robert Lewis
Feb 2 at 4:23
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
The equation may be transformed to a linear one as follows:
From
$dfrac{dy}{dx} + ytan x = y^3 cos x, tag 1$
write, after a multiplication by $y^{-3}$,
$y^{-3}dfrac{dy}{dx} + y^{-2}tan x = cos x, tag 2$
set
$z = y^{-2}; tag 3$
then
$dfrac{dz}{dx} = -2y^{-3} dfrac{dy}{dx}; tag 4$
(2) may thus be written
$-dfrac{1}{2} dfrac{dz}{dx} + z tan x = cos x, tag 5$
that is,
$dfrac{dz}{dx} -2(tan x)z = -2cos x, tag 6$
a linear equation with a known solution, which I leave to my readers to discover; it's all over the literature, and all over this website.
answered Feb 2 at 3:56
Robert LewisRobert Lewis
48.9k23168
$endgroup$
$begingroup$
Please don't answer blatant PSQs, it's unhealthy for the site. Instead, I'd suggest you prepare your answer in advance, even leave it here if need be and request the OP to put effort in, at which point after they do so you can upload your answer.
$endgroup$
– Rhys Hughes
Feb 2 at 4:01
$begingroup$
@RhysHughes: which side?
$endgroup$
– Robert Lewis
Feb 2 at 4:02
1
$begingroup$
Lol typo my bad. Typing on a tablet with autocorrect is clunky as usual.
$endgroup$
– Rhys Hughes
Feb 2 at 4:04
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The equation may be transformed to a linear one as follows:
From
$dfrac{dy}{dx} + ytan x = y^3 cos x, tag 1$
write, after a multiplication by $y^{-3}$,
$y^{-3}dfrac{dy}{dx} + y^{-2}tan x = cos x, tag 2$
set
$z = y^{-2}; tag 3$
then
$dfrac{dz}{dx} = -2y^{-3} dfrac{dy}{dx}; tag 4$
(2) may thus be written
$-dfrac{1}{2} dfrac{dz}{dx} + z tan x = cos x, tag 5$
that is,
$dfrac{dz}{dx} -2(tan x)z = -2cos x, tag 6$
a linear equation with a known solution, which I leave to my readers to discover; it's all over the literature, and all over this website.
answered Feb 2 at 3:56
Robert LewisRobert Lewis
48.9k23168
$endgroup$
$begingroup$
Please don't answer blatant PSQs, it's unhealthy for the site. Instead, I'd suggest you prepare your answer in advance, even leave it here if need be and request the OP to put effort in, at which point after they do so you can upload your answer.
$endgroup$
– Rhys Hughes
Feb 2 at 4:01
$begingroup$
@RhysHughes: which side?
$endgroup$
– Robert Lewis
Feb 2 at 4:02
1
$begingroup$
Lol typo my bad. Typing on a tablet with autocorrect is clunky as usual.
$endgroup$
– Rhys Hughes
Feb 2 at 4:04
add a comment |
$begingroup$
The equation may be transformed to a linear one as follows:
From
$dfrac{dy}{dx} + ytan x = y^3 cos x, tag 1$
write, after a multiplication by $y^{-3}$,
$y^{-3}dfrac{dy}{dx} + y^{-2}tan x = cos x, tag 2$
set
$z = y^{-2}; tag 3$
then
$dfrac{dz}{dx} = -2y^{-3} dfrac{dy}{dx}; tag 4$
(2) may thus be written
$-dfrac{1}{2} dfrac{dz}{dx} + z tan x = cos x, tag 5$
that is,
$dfrac{dz}{dx} -2(tan x)z = -2cos x, tag 6$
a linear equation with a known solution, which I leave to my readers to discover; it's all over the literature, and all over this website.
answered Feb 2 at 3:56
Robert LewisRobert Lewis
48.9k23168
$endgroup$
$begingroup$
Please don't answer blatant PSQs, it's unhealthy for the site. Instead, I'd suggest you prepare your answer in advance, even leave it here if need be and request the OP to put effort in, at which point after they do so you can upload your answer.
$endgroup$
– Rhys Hughes
Feb 2 at 4:01
$begingroup$
@RhysHughes: which side?
$endgroup$
– Robert Lewis
Feb 2 at 4:02
1
$begingroup$
Lol typo my bad. Typing on a tablet with autocorrect is clunky as usual.
$endgroup$
– Rhys Hughes
Feb 2 at 4:04
add a comment |
$begingroup$
The equation may be transformed to a linear one as follows:
From
$dfrac{dy}{dx} + ytan x = y^3 cos x, tag 1$
write, after a multiplication by $y^{-3}$,
$y^{-3}dfrac{dy}{dx} + y^{-2}tan x = cos x, tag 2$
set
$z = y^{-2}; tag 3$
then
$dfrac{dz}{dx} = -2y^{-3} dfrac{dy}{dx}; tag 4$
(2) may thus be written
$-dfrac{1}{2} dfrac{dz}{dx} + z tan x = cos x, tag 5$
that is,
$dfrac{dz}{dx} -2(tan x)z = -2cos x, tag 6$
a linear equation with a known solution, which I leave to my readers to discover; it's all over the literature, and all over this website.
answered Feb 2 at 3:56
Robert LewisRobert Lewis
48.9k23168
$endgroup$
The equation may be transformed to a linear one as follows:
From
$dfrac{dy}{dx} + ytan x = y^3 cos x, tag 1$
write, after a multiplication by $y^{-3}$,
$y^{-3}dfrac{dy}{dx} + y^{-2}tan x = cos x, tag 2$
set
$z = y^{-2}; tag 3$
then
$dfrac{dz}{dx} = -2y^{-3} dfrac{dy}{dx}; tag 4$
(2) may thus be written
$-dfrac{1}{2} dfrac{dz}{dx} + z tan x = cos x, tag 5$
that is,
$dfrac{dz}{dx} -2(tan x)z = -2cos x, tag 6$
a linear equation with a known solution, which I leave to my readers to discover; it's all over the literature, and all over this website.
answered Feb 2 at 3:56
Robert LewisRobert Lewis
48.9k23168
answered Feb 2 at 3:56
Robert LewisRobert Lewis
48.9k23168
answered Feb 2 at 3:56
Robert LewisRobert Lewis
48.9k23168
answered Feb 2 at 3:56
Robert LewisRobert Lewis
48.9k23168
48.9k23168
$begingroup$
Please don't answer blatant PSQs, it's unhealthy for the site. Instead, I'd suggest you prepare your answer in advance, even leave it here if need be and request the OP to put effort in, at which point after they do so you can upload your answer.
$endgroup$
– Rhys Hughes
Feb 2 at 4:01
$begingroup$
@RhysHughes: which side?
$endgroup$
– Robert Lewis
Feb 2 at 4:02
1
$begingroup$
Lol typo my bad. Typing on a tablet with autocorrect is clunky as usual.
$endgroup$
– Rhys Hughes
Feb 2 at 4:04
add a comment |
$begingroup$
Please don't answer blatant PSQs, it's unhealthy for the site. Instead, I'd suggest you prepare your answer in advance, even leave it here if need be and request the OP to put effort in, at which point after they do so you can upload your answer.
$endgroup$
– Rhys Hughes
Feb 2 at 4:01
$begingroup$
@RhysHughes: which side?
$endgroup$
– Robert Lewis
Feb 2 at 4:02
1
$begingroup$
Lol typo my bad. Typing on a tablet with autocorrect is clunky as usual.
$endgroup$
– Rhys Hughes
Feb 2 at 4:04
$begingroup$
Please don't answer blatant PSQs, it's unhealthy for the site. Instead, I'd suggest you prepare your answer in advance, even leave it here if need be and request the OP to put effort in, at which point after they do so you can upload your answer.
$endgroup$
– Rhys Hughes
Feb 2 at 4:01
$begingroup$
Please don't answer blatant PSQs, it's unhealthy for the site. Instead, I'd suggest you prepare your answer in advance, even leave it here if need be and request the OP to put effort in, at which point after they do so you can upload your answer.
$endgroup$
– Rhys Hughes
Feb 2 at 4:01
$begingroup$
@RhysHughes: which side?
$endgroup$
– Robert Lewis
Feb 2 at 4:02
$begingroup$
@RhysHughes: which side?
$endgroup$
– Robert Lewis
Feb 2 at 4:02
1
1
$begingroup$
Lol typo my bad. Typing on a tablet with autocorrect is clunky as usual.
$endgroup$
– Rhys Hughes
Feb 2 at 4:04
$begingroup$
Lol typo my bad. Typing on a tablet with autocorrect is clunky as usual.
$endgroup$
– Rhys Hughes
Feb 2 at 4:04
add a comment |
$begingroup$
Is that a demand? If so, then no; you solve it.
$endgroup$
– Mark Viola
Feb 2 at 3:51
$begingroup$
This is quite straightforward to solve. Show us you've put some effort into it and we'll help you where you got stuck.
$endgroup$
– Rhys Hughes
Feb 2 at 3:57
1
$begingroup$
Your question is headed for closure, since (1) you didn't write out the equation in $LaTeX$, which is inconvenient for your readers; (2) you didn't provide any context--information about why this is a problem of interest, or what you have tried. Not to worry, it takes a while to get the hang of the culture around here. Anyway, I've tried to give you a pointer in my answer below. Welcome to MSE, and Cheers!
$endgroup$
– Robert Lewis
Feb 2 at 4:00
$begingroup$
I also added the "differential-equations" tag to your post.
$endgroup$
– Robert Lewis
Feb 2 at 4:23