Please help me to solve the differential equation $$y''=\frac{1}{y^2}$$
Thank you very much!
Please help me to solve the differential equation $$y''=\frac{1}{y^2}$$
Thank you very much!
A start: The following is a standard trick. Multiply both sides by $y'$. Then the new left side is the derivative of $(1/2)(y')^2$ and the new right side is the derivative of $-1/y$. It follows that $$\frac{1}{2}(y')^2= -\frac{1}{y}+C$$ for some constant $C$. Solve for $y'$. You will get a couple of separable first-order differential equations.