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I want to get a particular solution to the differential equation $$ y''+2y'+2y=2e^x cos(x) $$ and therefore I would like to 'complexify' the right hand side. This means that I want to write the right hand side as $q(x)e^{\alpha x}$ with $q(x)$ a polynomial. How is this possible?

The solution should be $(1/4)e^x(\sin(x)+\cos(x))$ but I cannot see that.

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