What is the solution for y^{''}-36y=9xe^{6x} ?

The solution for y^{''}-36y=9xe^{6x} is y=c_{1}e^{6x}+c_{2}e^{-6x}+(3e^{6x}x^2)/8-(e^{6x}x)/(16)

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y^{''}-36y=9xe^{6x}

y^{^{''}} - 36 y = 9 x e^{6 x}

y = c_{1} e^{6 x} + c_{2} e^{- 6 x} + \frac{3 e ^{6 x} x ^{2}}{8} - \frac{e ^{6 x} x}{16}

Solution steps

y^{''} (x) - 36 y = 9 x e^{6 x}

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} e^{- 6 x} + \frac{3 e ^{6 x} x ^{2}}{8} - \frac{e ^{6 x} x}{16}

y = c_{1} e^{6 x} + c_{2} e^{- 6 x} + \frac{3 e ^{6 x} x ^{2}}{8} - \frac{e ^{6 x} x}{16}

31 y^{^{''}} + 800 y = 100 cos (4 t), y (0) = 0, y^{^{'}} (0) = 0

x^{^{''''}} + 2 x^{^{''}} + x = 4 t e^{t}

y^{^{''''}} - 4 y^{^{'''}} - 12 y^{^{''}} = 3 e^{5 x}

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

2 y^{^{''}} - 7 y^{^{'}} + 3 y = 4 x^{2}

What is the solution for y^{''}-36y=9xe^{6x} ?
The solution for y^{''}-36y=9xe^{6x} is y=c_{1}e^{6x}+c_{2}e^{-6x}+(3e^{6x}x^2)/8-(e^{6x}x)/(16)