How to solve the differential equation of the form $\ddot{x}-c_1 \frac{0.2x}{\sqrt{1+0.04x^2}}=0$?

Question

I was trying to get the equations of motion of a cube descending a curved inclined plane described by $0.1x^2$ and I got the folllowing ODE from Newton's 2nd Law: \begin{align*} \ddot{x}&=g\sin\alpha\\ \ddot{x}&=g\sin{[\tan^{-1}(0.2x)]}\\\\ \ddot{x}&-g\frac{0.2x}{\sqrt{1+0.04x^2}}=0 \end{align*} I thought about the linear pendulum ODE ($\ddot{\varphi}+c_1\varphi=0$), which can be solved via Laplace Transform, but this time it wasn't effective...