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

The solution for y^{''}-12y^'+36y=4xe^{6x} is y=c_{1}e^{6x}+c_{2}xe^{6x}+(2e^{6x}x^3)/3

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

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

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

Solution steps

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

Solve linear ODE:

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

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

n = 2 \sum \infty e^{3 - 2 n}

\int 3 (3 x + 9)^{3} d x

x \to 0 lim (\frac{sinh ( x ) - x}{x ^{3}})

e^{n \cdot x}

\frac{x ^{2}}{4}, \frac{- x + 6}{4}, - 3, 2

What is the solution for y^{''}-12y^'+36y=4xe^{6x} ?
The solution for y^{''}-12y^'+36y=4xe^{6x} is y=c_{1}e^{6x}+c_{2}xe^{6x}+(2e^{6x}x^3)/3