# Solving Nonlinear ODEs II

#### hatguy

##### New member
I need to solve the following ODE:

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#### Ackbach

##### Indicium Physicus
Staff member
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
If it is indeed what Ackbach says, try letting $u = \dfrac{x+y}{2x-y+1}$.

#### Ackbach

##### Indicium Physicus
Staff member
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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