Mixing
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ODE and linear substitution
I'm having a hard time solving the following differential equation:
$$dot{x}=frac{1}{t+2x}$$
I tried introducing $z = t+2x$, and so $dot{z}=1+2dot{x}$, and I got the following:
$$dot{z}=frac{2}{z}+1$$
Which is also not in a known form. What am I missing?
differential-equations
asked Nov 21 '18 at 13:21
galah92
25418
add a comment |
I'm having a hard time solving the following differential equation:
$$dot{x}=frac{1}{t+2x}$$
I tried introducing $z = t+2x$, and so $dot{z}=1+2dot{x}$, and I got the following:
$$dot{z}=frac{2}{z}+1$$
Which is also not in a known form. What am I missing?
differential-equations
asked Nov 21 '18 at 13:21
galah92
25418
1
$dfrac{z}{2+z} dz=dt$
– Nosrati
Nov 21 '18 at 13:28
1
This is a known form !
– Yves Daoust
Nov 21 '18 at 13:39
add a comment |
I'm having a hard time solving the following differential equation:
$$dot{x}=frac{1}{t+2x}$$
I tried introducing $z = t+2x$, and so $dot{z}=1+2dot{x}$, and I got the following:
$$dot{z}=frac{2}{z}+1$$
Which is also not in a known form. What am I missing?
differential-equations
asked Nov 21 '18 at 13:21
galah92
25418
I'm having a hard time solving the following differential equation:
$$dot{x}=frac{1}{t+2x}$$
I tried introducing $z = t+2x$, and so $dot{z}=1+2dot{x}$, and I got the following:
$$dot{z}=frac{2}{z}+1$$
Which is also not in a known form. What am I missing?
differential-equations
differential-equations
asked Nov 21 '18 at 13:21
galah92
25418
asked Nov 21 '18 at 13:21
galah92
25418
edited Nov 21 '18 at 13:27
asked Nov 21 '18 at 13:21
galah92
25418
asked Nov 21 '18 at 13:21
galah92
25418
asked Nov 21 '18 at 13:21
galah92
25418
25418
1
$dfrac{z}{2+z} dz=dt$
– Nosrati
Nov 21 '18 at 13:28
1
This is a known form !
– Yves Daoust
Nov 21 '18 at 13:39
add a comment |
1
$dfrac{z}{2+z} dz=dt$
– Nosrati
Nov 21 '18 at 13:28
1
This is a known form !
– Yves Daoust
Nov 21 '18 at 13:39
1
1
$dfrac{z}{2+z} dz=dt$
– Nosrati
Nov 21 '18 at 13:28
$dfrac{z}{2+z} dz=dt$
– Nosrati
Nov 21 '18 at 13:28
1
1
This is a known form !
– Yves Daoust
Nov 21 '18 at 13:39
This is a known form !
– Yves Daoust
Nov 21 '18 at 13:39
add a comment |
1 Answer
1
active
oldest
votes
You have a separable differential equation $$ dot {z}=frac {z+2}{z}$$
$$ int frac {zdz}{z+2}=int dt$$
answered Nov 21 '18 at 14:12
Mohammad Riazi-Kermani
41k42059
add a comment |
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1 Answer
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1 Answer
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active
oldest
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active
oldest
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active
oldest
votes
You have a separable differential equation $$ dot {z}=frac {z+2}{z}$$
$$ int frac {zdz}{z+2}=int dt$$
answered Nov 21 '18 at 14:12
Mohammad Riazi-Kermani
41k42059
add a comment |
You have a separable differential equation $$ dot {z}=frac {z+2}{z}$$
$$ int frac {zdz}{z+2}=int dt$$
answered Nov 21 '18 at 14:12
Mohammad Riazi-Kermani
41k42059
add a comment |
You have a separable differential equation $$ dot {z}=frac {z+2}{z}$$
$$ int frac {zdz}{z+2}=int dt$$
answered Nov 21 '18 at 14:12
Mohammad Riazi-Kermani
41k42059
You have a separable differential equation $$ dot {z}=frac {z+2}{z}$$
$$ int frac {zdz}{z+2}=int dt$$
answered Nov 21 '18 at 14:12
Mohammad Riazi-Kermani
41k42059
answered Nov 21 '18 at 14:12
Mohammad Riazi-Kermani
41k42059
answered Nov 21 '18 at 14:12
Mohammad Riazi-Kermani
41k42059
answered Nov 21 '18 at 14:12
Mohammad Riazi-Kermani
41k42059
41k42059
add a comment |
add a comment |
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1
$dfrac{z}{2+z} dz=dt$
– Nosrati
Nov 21 '18 at 13:28
1
This is a known form !
– Yves Daoust
Nov 21 '18 at 13:39