Cauchy's problem. Equation of mathematical physics

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$$U_{tt} = \Delta U + x^3 - 3xy^2$$

$$U|_{t=0} = e^x \cos y$$

$$U_t|_{t=0} = e^y \sin x$$

Help me, please, with solution of this equation. Can you prompt me algorithm to find the solution? I know, that I have to use Poisson's formula, but I can't integrate it.