What is the solution for y^{''}-12y^'+36y=10e^{6x} ?

The solution for y^{''}-12y^'+36y=10e^{6x} is y=c_{1}e^{6x}+c_{2}xe^{6x}+5x^2e^{6x}

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y^{''}-12y^'+36y=10e^{6x}

y^{^{''}} - 12 y^{^{'}} + 36 y = 10 e^{6 x}

y = c_{1} e^{6 x} + c_{2} x e^{6 x} + 5 x^{2} e^{6 x}

Solution steps

y^{''} (x) - 12 y^{'} (x) + 36 y = 10 e^{6 x}

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} x e^{6 x} + 5 x^{2} e^{6 x}

y = c_{1} e^{6 x} + c_{2} x e^{6 x} + 5 x^{2} e^{6 x}

y^{^{''}} - 2 y^{^{'}} + y = 14 x^{\frac{2}{3}} e^{x}

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 6 y = 4 e^{2 x}

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} - y = t^{2} e^{t}

11 x^{^{''}} + 112.5 x = 5 e^{- t}, x (0) = 0, x^{^{'}} (0) = 0

y^{^{''}} + 3 y^{^{'}} + 2 y = 6 e^{- t}, y (0) = 1, y^{^{'}} (0) = 2

What is the solution for y^{''}-12y^'+36y=10e^{6x} ?
The solution for y^{''}-12y^'+36y=10e^{6x} is y=c_{1}e^{6x}+c_{2}xe^{6x}+5x^2e^{6x}