What is the solution for y^{''}+2y^'+10y=x^2e^{-x}cos(3x) ?

The solution for y^{''}+2y^'+10y=x^2e^{-x}cos(3x) is

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y^{''}+2y^'+10y=x^2e^{-x}cos(3x)

y^{^{''}} + 2 y^{^{'}} + 10 y = x^{2} e^{- x} cos (3 x)

y = e^{- x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + \frac{- e ^{- x} cos ( 3 x ) ( - 18 x ^{2} cos ( 6 x ) + 6 x sin ( 6 x ) + cos ( 6 x ) ) + e ^{- x} sin ( 3 x ) ( 72 x ^{3} cos ^{2} ( 3 x ) - 36 x ^{3} cos ( 6 x ) + 18 x ^{2} sin ( 6 x ) - sin ( 6 x ) + 6 x cos ( 6 x ) )}{648}

Solution steps

y^{''} (x) + 2 y^{'} (x) + 10 y = x^{2} e^{- x} cos (3 x)

Solve linear ODE:

y = e^{- x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + \frac{- e ^{- x} cos ( 3 x ) ( - 18 x ^{2} cos ( 6 x ) + 6 x sin ( 6 x ) + cos ( 6 x ) ) + e ^{- x} sin ( 3 x ) ( 72 x ^{3} cos ^{2} ( 3 x ) - 36 x ^{3} cos ( 6 x ) + 18 x ^{2} sin ( 6 x ) - sin ( 6 x ) + 6 x cos ( 6 x ) )}{648}

y = e^{- x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + \frac{- e ^{- x} cos ( 3 x ) ( - 18 x ^{2} cos ( 6 x ) + 6 x sin ( 6 x ) + cos ( 6 x ) ) + e ^{- x} sin ( 3 x ) ( 72 x ^{3} cos ^{2} ( 3 x ) - 36 x ^{3} cos ( 6 x ) + 18 x ^{2} sin ( 6 x ) - sin ( 6 x ) + 6 x cos ( 6 x ) )}{648}

y^{^{''}} + 4 y = 9 t, y (0) = 0, y^{^{'}} (0) = 7

5 y^{^{''}} - 15 y = 10 e^{x}

y^{^{''}} + 2 y^{^{'}} + y = e^{- x} (2 x - 5)

y^{^{''}} - y^{^{'}} = 16 e^{3 x}

y^{^{''}} + 2 y^{^{'}} + 2 y = 5 sin (x) - 10 x e^{x}

What is the solution for y^{''}+2y^'+10y=x^2e^{-x}cos(3x) ?
The solution for y^{''}+2y^'+10y=x^2e^{-x}cos(3x) is