Find third-order ,homogenous, Euler differential equation such that $\sin(2\ln x)$ is a solution and the solutions are bounded in $x>0$.

Question

Find third-order ,homogenous, Euler differential equation such that $\sin(2\ln x)$ is a solution and the solutions are bounded in $x>0$.

Since $\sin(2\ln x)$ is a solution then $\cos(2\ln x)$.

The third solution will be $x^r$ such that $x^r<M\in \mathbb{R} \implies r=0$.

Then the characteristic polynomial is $r^3+4r$

My problem is how to get an Euler differential equation.

Help is welcome , thanks !