# Non-linear first order ODE

1. Feb 26, 2015

### joshmccraney

1. The problem statement, all variables and given/known data
$$y' y + \frac{y}{x} = 1 - 2x$$

2. Relevant equations
nothing comes to mind

3. The attempt at a solution
i've guessed a quadratic but that didn't work. now i'm stuck. any ideas? also, this is not homework, but a problem I am working on.

Thanks!

2. Feb 26, 2015

### BiGyElLoWhAt

Is y y(x)?

3. Feb 26, 2015

### joshmccraney

sorry, yes, $y = y(x)$

4. Feb 26, 2015

### LCKurtz

5. Feb 26, 2015

### joshmccraney

This is an interesting website. When I perform their substitutions I arrive at $$y \frac{dy}{dz} -y = \frac{2x - 1}{\ln | x |} : z:= \int -\frac{1}{x} dx$$ but from here their table provides no further help. Do you suppose this problem has never been analytically solved?

6. Feb 26, 2015

### LCKurtz

I have no idea but it wouldn't surprise me.

7. Feb 27, 2015

### BiGyElLoWhAt

This did appear deceptively easy at first glance =/