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## Homework Statement

[tex]yy''-y'^2 = y^2lny[/tex]

## The Attempt at a Solution

well, since the equation is of the form [itex]f(y,y',y'')=0[/itex] I turn it into the form [itex]f(y,p,p dp/dy)=0[/itex].

After those substitutions are made, we'll have the following equation:

[tex]yp (\frac{dp}{dy})-p^2-y^2 lny=0[/tex]

which is a Bernoulli equation that can be solved easily. the solution of this ODE is:

[tex]p^2=y^2lny+cy^2[/tex]

Here's where I'm stuck, because If I substitute y'=p again I'll have an ODE that I don't know how to solve it, I guess the general solution will be parametric, but I don't know how to proceed from this step.

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