What is the solution for y^{''}-12y^'+36y=4e^{6x} ?

The solution for y^{''}-12y^'+36y=4e^{6x} is y=c_{1}e^{6x}+c_{2}xe^{6x}+2x^2e^{6x}

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y^{''}-12y^'+36y=4e^{6x}

y^{^{''}} - 12 y^{^{'}} + 36 y = 4 e^{6 x}

y = c_{1} e^{6 x} + c_{2} x e^{6 x} + 2 x^{2} e^{6 x}

Solution steps

y^{''} (x) - 12 y^{'} (x) + 36 y = 4 e^{6 x}

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} x e^{6 x} + 2 x^{2} e^{6 x}

y = c_{1} e^{6 x} + c_{2} x e^{6 x} + 2 x^{2} e^{6 x}

y^{^{''}} + 3 y^{^{'}} + 5 y = sin (t), y (0) = 1, y (0) = 0

x^{^{''}} - 25 x = 3 e^{2 t}

(D^{3} + 3 D^{2} - 4) y = x e^{- 2 x}

y^{^{''}} - y = 1, y (0) = 0

y^{^{''}} + 4 y^{^{'}} + 6 y = 1, + e^{-} t y (0) = 0, y^{^{'}} (0) = 0

What is the solution for y^{''}-12y^'+36y=4e^{6x} ?
The solution for y^{''}-12y^'+36y=4e^{6x} is y=c_{1}e^{6x}+c_{2}xe^{6x}+2x^2e^{6x}