Second order \(\frac{d^2y}{dx^2}\) differential equations

Equations of type1, \(\frac{d^2y}{dx^2}=f(y)\)

Equations of type2, \(\frac{d^2y}{dx^2}=f(\frac{dy}{dx})\)

Equations of type3, \(f(x,\frac{dy}{dx},\frac{d^2y}{dx^2})=0\)

Equations of type4, \(f(y,\frac{dy}{dx},\frac{d^2y}{dx^2})=0\)