What is the solution for y^{''}-12y^'+36y=5e^2x ?

The solution for y^{''}-12y^'+36y=5e^2x is y=c_{1}e^{6x}+c_{2}xe^{6x}+(5e^2x)/(36)+(5e^2)/(108)

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y^{''}-12y^'+36y=5e^2x

y^{^{''}} - 12 y^{^{'}} + 36 y = 5 e^{2} x

y = c_{1} e^{6 x} + c_{2} x e^{6 x} + \frac{5 e ^{2} x}{36} + \frac{5 e ^{2}}{108}

Solution steps

y^{''} (x) - 12 y^{'} (x) + 36 y = 5 e^{2} x

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} x e^{6 x} + \frac{5 e ^{2} x}{36} + \frac{5 e ^{2}}{108}

y = c_{1} e^{6 x} + c_{2} x e^{6 x} + \frac{5 e ^{2} x}{36} + \frac{5 e ^{2}}{108}

What is the solution for y^{''}-12y^'+36y=5e^2x ?
The solution for y^{''}-12y^'+36y=5e^2x is y=c_{1}e^{6x}+c_{2}xe^{6x}+(5e^2x)/(36)+(5e^2)/(108)