${u}_{xx}+{y}^{2}u=\mathrm{sin}2x$

I want to solve the non homogeneous differential equation

$$\frac{{\mathrm{\partial}}^{2}u}{\mathrm{\partial}{x}^{2}}+{y}^{2}u=\mathrm{sin}2x.$$

I have tried to solve it by method of separable of variables. But unfortunately, not able to find out the solution. Please give me some hints to solve it.

I want to solve the non homogeneous differential equation

$$\frac{{\mathrm{\partial}}^{2}u}{\mathrm{\partial}{x}^{2}}+{y}^{2}u=\mathrm{sin}2x.$$

I have tried to solve it by method of separable of variables. But unfortunately, not able to find out the solution. Please give me some hints to solve it.