What is the solution for y^{''}+2y^'+2y=2(x+1)^2 ?

The solution for y^{''}+2y^'+2y=2(x+1)^2 is y=e^{-x}(c_{1}cos(x)+c_{2}sin(x))+x^2

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y^{''}+2y^'+2y=2(x+1)^2

y^{^{''}} + 2 y^{^{'}} + 2 y = 2 (x + 1)^{2}

y = e^{- x} (c_{1} cos (x) + c_{2} sin (x)) + x^{2}

Solution steps

y^{''} (x) + 2 y^{'} (x) + 2 y = 2 (x + 1)^{2}

Solve linear ODE:

y = e^{- x} (c_{1} cos (x) + c_{2} sin (x)) + x^{2}

y = e^{- x} (c_{1} cos (x) + c_{2} sin (x)) + x^{2}

What is the solution for y^{''}+2y^'+2y=2(x+1)^2 ?
The solution for y^{''}+2y^'+2y=2(x+1)^2 is y=e^{-x}(c_{1}cos(x)+c_{2}sin(x))+x^2