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Solving Nonlinear ODEs II

hatguy

New member
Dec 25, 2012
3
I need to solve the following ODE:



but i can't figure out a way to. Please help!
 
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Ackbach

Indicium Physicus
Staff member
Jan 26, 2012
4,197
Regarding 3:
Did you mean
$$y'=e^{ \frac{x+y}{2x-y+1}}+\frac{3y-1}{3x+1}?$$
The absence of a closing parenthesis in the numerator of the argument of the exponential function makes your meaning unclear.
 

Jester

Well-known member
MHB Math Helper
Jan 26, 2012
183
If it is indeed what Ackbach says, try letting $u = \dfrac{x+y}{2x-y+1}$.
 

Ackbach

Indicium Physicus
Staff member
Jan 26, 2012
4,197
If it is indeed what Ackbach says, try letting $u = \dfrac{x+y}{2x-y+1}$.
Nice! The result is separable. I get
$$\frac{e^{-u}}{u+1}\,u'=\frac{1}{3x+1}.$$

Of course, the integral on the left is not elementary. Oh, well.
 
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