Nonlinear second order differential equation

[JulieK]

What is the solution of the follwoing differential equation

\frac{\partial^{2}y}{\partial x^{2}}-ay^{-1}\frac{dy}{dx}=0

where a is a constant.

 

[pasmith]

What is the solution of the follwoing differential equation

\frac{\partial^{2}y}{\partial x^{2}}-ay^{-1}\frac{dy}{dx}=0

where a is a constant.

Use the identity
\frac{\mathrm{d}^2y}{\mathrm{d} x^2} = \frac{\mathrm{d}y&#039;}{\mathrm{d}x} =<br /> \frac{\mathrm{d}y&#039;}{\mathrm{d}y}\frac{\mathrm{d}y}{\mathrm{d}x} = y&#039;\frac{\mathrm{d}y&#039;}{\mathrm{d}y}
to find y&#039; = \frac{\mathrm{d}y}{\mathrm{d}x} as a function of y. Then use separation of variables.

 

[JulieK]

Thank you