How can I solve a differential equation of this type?

$$
\frac{\partial^2 f[x]}{\partial x^2}\frac{\partial g[x]}{\partial x}-\frac{\partial f[x]}{\partial x}\frac{\partial^2 g[x]}{\partial x^2}=0
$$

I believe the following notation is equivalent:

$$
f''[x]g'[x]-f'[x]g''[x]=0
$$