Mixing
A difficult differential equation $ y(2x^4+y)frac{dy}{dx} = (1-4xy^2)x^2$
up vote
2
down vote
favorite
How to solve the following differential equation?
$$ y(2x^4+y)dfrac{dy}{dx} = (1-4xy^2)x^2$$
No clue as to how to even begin. Hints?
calculus differential-equations
asked Sep 11 '13 at 4:14
Parth Thakkar
2,71521635
add a comment |
up vote
2
down vote
favorite
How to solve the following differential equation?
$$ y(2x^4+y)dfrac{dy}{dx} = (1-4xy^2)x^2$$
No clue as to how to even begin. Hints?
calculus differential-equations
asked Sep 11 '13 at 4:14
Parth Thakkar
2,71521635
add a comment |
up vote
2
down vote
favorite
up vote
2
down vote
favorite
How to solve the following differential equation?
$$ y(2x^4+y)dfrac{dy}{dx} = (1-4xy^2)x^2$$
No clue as to how to even begin. Hints?
calculus differential-equations
asked Sep 11 '13 at 4:14
Parth Thakkar
2,71521635
How to solve the following differential equation?
$$ y(2x^4+y)dfrac{dy}{dx} = (1-4xy^2)x^2$$
No clue as to how to even begin. Hints?
calculus differential-equations
calculus differential-equations
asked Sep 11 '13 at 4:14
Parth Thakkar
2,71521635
asked Sep 11 '13 at 4:14
Parth Thakkar
2,71521635
asked Sep 11 '13 at 4:14
Parth Thakkar
2,71521635
asked Sep 11 '13 at 4:14
Parth Thakkar
2,71521635
asked Sep 11 '13 at 4:14
Parth Thakkar
2,71521635
2,71521635
add a comment |
add a comment |
3 Answers
3
active
oldest
votes
up vote
5
down vote
accepted
Hint: it's an exact differential equation.
answered Sep 11 '13 at 4:16
Robert Israel
313k23206452
Please drop some more hint. This doesn't seem so straight forward to me.
– Parth Thakkar
Sep 11 '13 at 4:36
Well, I am familiar, but that's just it. I am only familiar. I haven't mastered it yet. I tried to bring it in an exact form, but I couldn't.
– Parth Thakkar
Sep 11 '13 at 5:09
1
Wait, I think there's some terminology issue here. By Exact method, do you mean writing the equation so that it is expressed as $ d( text{blob} ) = text{something integrable}$? I just googled the 'exact' method and what I got was something with partial derivatives. That, I do not know.
– Parth Thakkar
Sep 11 '13 at 5:12
1
You are writing $M dx + N dy = 0$: see tutorial.math.lamar.edu/Classes/DE/Exact.aspx for worked examples. Regards
– Amzoti
Sep 11 '13 at 5:19
Thanks a lot for that resource. Just began reading and seems nice! +1!
– Parth Thakkar
Sep 11 '13 at 5:27
|
show 1 more comment
up vote
3
down vote
$$y(2x^4+y)frac{dy}{dx}=(1-4xy^2)x^2$$
$$2x^4yfrac{dy}{dx}+y^2frac{dy}{dx}=x^2-4x^3 y^2$$
$$2x^4yfrac{dy}{dx}+4x^3y^2+y^2frac{dy}{dx}=x^2$$
$$frac{d}{dx}(x^4 y^2)+y^2frac{dy}{dx}=x^2$$
$$x^4y^2+frac{y^3}{3}=frac{x^3}{3}+C$$
edited Mar 5 at 21:33
mucciolo
1,9741819
answered Mar 5 at 21:16
Ibrahim
311
add a comment |
up vote
0
down vote
Hint:
Apply $M(x,y)=frac{du}{dx}$ and $ N(x,y)=frac{du}{dy}$
edited Mar 18 '17 at 10:42
SaudiBombsYemen
95110
answered Sep 11 '13 at 12:39
Angelo
434
add a comment |
3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
5
down vote
accepted
Hint: it's an exact differential equation.
answered Sep 11 '13 at 4:16
Robert Israel
313k23206452
Please drop some more hint. This doesn't seem so straight forward to me.
– Parth Thakkar
Sep 11 '13 at 4:36
Well, I am familiar, but that's just it. I am only familiar. I haven't mastered it yet. I tried to bring it in an exact form, but I couldn't.
– Parth Thakkar
Sep 11 '13 at 5:09
1
Wait, I think there's some terminology issue here. By Exact method, do you mean writing the equation so that it is expressed as $ d( text{blob} ) = text{something integrable}$? I just googled the 'exact' method and what I got was something with partial derivatives. That, I do not know.
– Parth Thakkar
Sep 11 '13 at 5:12
1
You are writing $M dx + N dy = 0$: see tutorial.math.lamar.edu/Classes/DE/Exact.aspx for worked examples. Regards
– Amzoti
Sep 11 '13 at 5:19
Thanks a lot for that resource. Just began reading and seems nice! +1!
– Parth Thakkar
Sep 11 '13 at 5:27
|
show 1 more comment
up vote
5
down vote
accepted
Hint: it's an exact differential equation.
answered Sep 11 '13 at 4:16
Robert Israel
313k23206452
Please drop some more hint. This doesn't seem so straight forward to me.
– Parth Thakkar
Sep 11 '13 at 4:36
Well, I am familiar, but that's just it. I am only familiar. I haven't mastered it yet. I tried to bring it in an exact form, but I couldn't.
– Parth Thakkar
Sep 11 '13 at 5:09
1
Wait, I think there's some terminology issue here. By Exact method, do you mean writing the equation so that it is expressed as $ d( text{blob} ) = text{something integrable}$? I just googled the 'exact' method and what I got was something with partial derivatives. That, I do not know.
– Parth Thakkar
Sep 11 '13 at 5:12
1
You are writing $M dx + N dy = 0$: see tutorial.math.lamar.edu/Classes/DE/Exact.aspx for worked examples. Regards
– Amzoti
Sep 11 '13 at 5:19
Thanks a lot for that resource. Just began reading and seems nice! +1!
– Parth Thakkar
Sep 11 '13 at 5:27
|
show 1 more comment
up vote
5
down vote
accepted
up vote
5
down vote
accepted
Hint: it's an exact differential equation.
answered Sep 11 '13 at 4:16
Robert Israel
313k23206452
Hint: it's an exact differential equation.
answered Sep 11 '13 at 4:16
Robert Israel
313k23206452
answered Sep 11 '13 at 4:16
Robert Israel
313k23206452
answered Sep 11 '13 at 4:16
Robert Israel
313k23206452
answered Sep 11 '13 at 4:16
Robert Israel
313k23206452
313k23206452
Please drop some more hint. This doesn't seem so straight forward to me.
– Parth Thakkar
Sep 11 '13 at 4:36
Well, I am familiar, but that's just it. I am only familiar. I haven't mastered it yet. I tried to bring it in an exact form, but I couldn't.
– Parth Thakkar
Sep 11 '13 at 5:09
1
Wait, I think there's some terminology issue here. By Exact method, do you mean writing the equation so that it is expressed as $ d( text{blob} ) = text{something integrable}$? I just googled the 'exact' method and what I got was something with partial derivatives. That, I do not know.
– Parth Thakkar
Sep 11 '13 at 5:12
1
You are writing $M dx + N dy = 0$: see tutorial.math.lamar.edu/Classes/DE/Exact.aspx for worked examples. Regards
– Amzoti
Sep 11 '13 at 5:19
Thanks a lot for that resource. Just began reading and seems nice! +1!
– Parth Thakkar
Sep 11 '13 at 5:27
|
show 1 more comment
Please drop some more hint. This doesn't seem so straight forward to me.
– Parth Thakkar
Sep 11 '13 at 4:36
Well, I am familiar, but that's just it. I am only familiar. I haven't mastered it yet. I tried to bring it in an exact form, but I couldn't.
– Parth Thakkar
Sep 11 '13 at 5:09
1
Wait, I think there's some terminology issue here. By Exact method, do you mean writing the equation so that it is expressed as $ d( text{blob} ) = text{something integrable}$? I just googled the 'exact' method and what I got was something with partial derivatives. That, I do not know.
– Parth Thakkar
Sep 11 '13 at 5:12
1
You are writing $M dx + N dy = 0$: see tutorial.math.lamar.edu/Classes/DE/Exact.aspx for worked examples. Regards
– Amzoti
Sep 11 '13 at 5:19
Thanks a lot for that resource. Just began reading and seems nice! +1!
– Parth Thakkar
Sep 11 '13 at 5:27
Please drop some more hint. This doesn't seem so straight forward to me.
– Parth Thakkar
Sep 11 '13 at 4:36
Please drop some more hint. This doesn't seem so straight forward to me.
– Parth Thakkar
Sep 11 '13 at 4:36
Well, I am familiar, but that's just it. I am only familiar. I haven't mastered it yet. I tried to bring it in an exact form, but I couldn't.
– Parth Thakkar
Sep 11 '13 at 5:09
Well, I am familiar, but that's just it. I am only familiar. I haven't mastered it yet. I tried to bring it in an exact form, but I couldn't.
– Parth Thakkar
Sep 11 '13 at 5:09
1
1
Wait, I think there's some terminology issue here. By Exact method, do you mean writing the equation so that it is expressed as $ d( text{blob} ) = text{something integrable}$? I just googled the 'exact' method and what I got was something with partial derivatives. That, I do not know.
– Parth Thakkar
Sep 11 '13 at 5:12
Wait, I think there's some terminology issue here. By Exact method, do you mean writing the equation so that it is expressed as $ d( text{blob} ) = text{something integrable}$? I just googled the 'exact' method and what I got was something with partial derivatives. That, I do not know.
– Parth Thakkar
Sep 11 '13 at 5:12
1
1
You are writing $M dx + N dy = 0$: see tutorial.math.lamar.edu/Classes/DE/Exact.aspx for worked examples. Regards
– Amzoti
Sep 11 '13 at 5:19
You are writing $M dx + N dy = 0$: see tutorial.math.lamar.edu/Classes/DE/Exact.aspx for worked examples. Regards
– Amzoti
Sep 11 '13 at 5:19
Thanks a lot for that resource. Just began reading and seems nice! +1!
– Parth Thakkar
Sep 11 '13 at 5:27
Thanks a lot for that resource. Just began reading and seems nice! +1!
– Parth Thakkar
Sep 11 '13 at 5:27
|
show 1 more comment
up vote
3
down vote
$$y(2x^4+y)frac{dy}{dx}=(1-4xy^2)x^2$$
$$2x^4yfrac{dy}{dx}+y^2frac{dy}{dx}=x^2-4x^3 y^2$$
$$2x^4yfrac{dy}{dx}+4x^3y^2+y^2frac{dy}{dx}=x^2$$
$$frac{d}{dx}(x^4 y^2)+y^2frac{dy}{dx}=x^2$$
$$x^4y^2+frac{y^3}{3}=frac{x^3}{3}+C$$
edited Mar 5 at 21:33
mucciolo
1,9741819
answered Mar 5 at 21:16
Ibrahim
311
add a comment |
up vote
3
down vote
$$y(2x^4+y)frac{dy}{dx}=(1-4xy^2)x^2$$
$$2x^4yfrac{dy}{dx}+y^2frac{dy}{dx}=x^2-4x^3 y^2$$
$$2x^4yfrac{dy}{dx}+4x^3y^2+y^2frac{dy}{dx}=x^2$$
$$frac{d}{dx}(x^4 y^2)+y^2frac{dy}{dx}=x^2$$
$$x^4y^2+frac{y^3}{3}=frac{x^3}{3}+C$$
edited Mar 5 at 21:33
mucciolo
1,9741819
answered Mar 5 at 21:16
Ibrahim
311
add a comment |
up vote
3
down vote
up vote
3
down vote
$$y(2x^4+y)frac{dy}{dx}=(1-4xy^2)x^2$$
$$2x^4yfrac{dy}{dx}+y^2frac{dy}{dx}=x^2-4x^3 y^2$$
$$2x^4yfrac{dy}{dx}+4x^3y^2+y^2frac{dy}{dx}=x^2$$
$$frac{d}{dx}(x^4 y^2)+y^2frac{dy}{dx}=x^2$$
$$x^4y^2+frac{y^3}{3}=frac{x^3}{3}+C$$
edited Mar 5 at 21:33
mucciolo
1,9741819
answered Mar 5 at 21:16
Ibrahim
311
$$y(2x^4+y)frac{dy}{dx}=(1-4xy^2)x^2$$
$$2x^4yfrac{dy}{dx}+y^2frac{dy}{dx}=x^2-4x^3 y^2$$
$$2x^4yfrac{dy}{dx}+4x^3y^2+y^2frac{dy}{dx}=x^2$$
$$frac{d}{dx}(x^4 y^2)+y^2frac{dy}{dx}=x^2$$
$$x^4y^2+frac{y^3}{3}=frac{x^3}{3}+C$$
edited Mar 5 at 21:33
mucciolo
1,9741819
answered Mar 5 at 21:16
Ibrahim
311
edited Mar 5 at 21:33
mucciolo
1,9741819
edited Mar 5 at 21:33
mucciolo
1,9741819
edited Mar 5 at 21:33
mucciolo
1,9741819
1,9741819
answered Mar 5 at 21:16
Ibrahim
311
answered Mar 5 at 21:16
Ibrahim
311
answered Mar 5 at 21:16
Ibrahim
311
311
add a comment |
add a comment |
up vote
0
down vote
Hint:
Apply $M(x,y)=frac{du}{dx}$ and $ N(x,y)=frac{du}{dy}$
edited Mar 18 '17 at 10:42
SaudiBombsYemen
95110
answered Sep 11 '13 at 12:39
Angelo
434
add a comment |
up vote
0
down vote
Hint:
Apply $M(x,y)=frac{du}{dx}$ and $ N(x,y)=frac{du}{dy}$
edited Mar 18 '17 at 10:42
SaudiBombsYemen
95110
answered Sep 11 '13 at 12:39
Angelo
434
add a comment |
up vote
0
down vote
up vote
0
down vote
Hint:
Apply $M(x,y)=frac{du}{dx}$ and $ N(x,y)=frac{du}{dy}$
edited Mar 18 '17 at 10:42
SaudiBombsYemen
95110
answered Sep 11 '13 at 12:39
Angelo
434
Hint:
Apply $M(x,y)=frac{du}{dx}$ and $ N(x,y)=frac{du}{dy}$
edited Mar 18 '17 at 10:42
SaudiBombsYemen
95110
answered Sep 11 '13 at 12:39
Angelo
434
edited Mar 18 '17 at 10:42
SaudiBombsYemen
95110
edited Mar 18 '17 at 10:42
SaudiBombsYemen
95110
edited Mar 18 '17 at 10:42
SaudiBombsYemen
95110
95110
answered Sep 11 '13 at 12:39
Angelo
434
answered Sep 11 '13 at 12:39
Angelo
434
answered Sep 11 '13 at 12:39
Angelo
434
434
add a comment |
add a comment |
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