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

The solution for y^{''}-12y^'+36y=6e^{6x} is y=c_{1}e^{6x}+c_{2}xe^{6x}+3x^2e^{6x}

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

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

y = c_{1} e^{6 x} + c_{2} x e^{6 x} + 3 x^{2} e^{6 x}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} x e^{6 x} + 3 x^{2} e^{6 x}

y = c_{1} e^{6 x} + c_{2} x e^{6 x} + 3 x^{2} e^{6 x}

y^{^{'''}} - y^{^{'}} = 3 cos (x)

y^{^{''}} - y^{^{'}} - 2 y = 3 x + 4

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

y^{^{''}} + 4 y = \frac{e ^{2 x}}{x}

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

What is the solution for y^{''}-12y^'+36y=6e^{6x} ?
The solution for y^{''}-12y^'+36y=6e^{6x} is y=c_{1}e^{6x}+c_{2}xe^{6x}+3x^2e^{6x}