Hi, can someone please help me with the following ODE? I need to find the general solution.(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

y = xy' + \frac{1}{{y'}}

[/tex]

Rearranging I get a quadratic in dy/dx.

[tex]

x\left( {\frac{{dy}}{{dx}}} \right)^2 - y\left( {\frac{{dy}}{{dx}}} \right) + 1 = 0

[/tex]

[tex]

\frac{{dy}}{{dx}} = \frac{{y \pm \sqrt {y^2 - 4x} }}{{2x}}

[/tex]

I don't know what to do from this point nor am I sure if I've started the right way. Any help would be good thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# First order ODE

**Physics Forums | Science Articles, Homework Help, Discussion**