# u_(xx)+y^2u= sin2x I want to solve the non homogeneous differential equation (del^2 u)/( del x^2}+y^2u= sin 2x.

${u}_{xx}+{y}^{2}u=\mathrm{sin}2x$
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.
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lipovicai1w
Use the method of undetermined characteristics and the methods from ODE's. $u=v+w$ where $v$ solves ${v}_{xx}+{y}^{2}v=0$ and $w=A\left(y\right)\mathrm{sin}\left(2x\right)+B\left(y\right)\mathrm{cos}\left(2x\right)$