What is the general solution of differential equation $y\frac{d^{2}y}{dx^2} - (\frac{dy}{dx})^2 = y^2 log(y)$ What is the general solution of differential equation $y\frac{d^{2}y}{dx^2} - (\frac{dy}{dx})^2 = y^2 log(y)$.
The answer to this DE is $log(y) = c_1 e^x + c_2 e^{-x}$
I don't know the method to solve differential equation with degree more than 1. Please tell me how to solve these types of equations.

Hint.  The equation can be written as
$$\frac{d}{dx}\Bigl(\frac{\frac{dy}{dx}}{y}\Bigr)=\log x\ .$$
There is in general no specific procedure for solving this kind of thing and you have to rely on "spotting" something like the above.
BTW I don't think the answer you have given is correct.  Probably the $\log x$ should be $\log y$ as suggested by LutzL.
