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

The solution for y^{''}-36y=9e^{6x} is y=c_{1}e^{6x}+c_{2}e^{-6x}+(3e^{6x}x)/4

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

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

y = c_{1} e^{6 x} + c_{2} e^{- 6 x} + \frac{3 e ^{6 x} x}{4}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} e^{- 6 x} + \frac{3 e ^{6 x} x}{4}

y = c_{1} e^{6 x} + c_{2} e^{- 6 x} + \frac{3 e ^{6 x} x}{4}

\frac{d ^{2} y}{d x ^{2}} + 4 y = 8

y^{^{''}} - 4 y^{^{'}} + 3 y = 4 cos (x) - 3 sin (x)

y^{^{'''}} - 3 y^{^{''}} - y^{^{'}} + 3 y = 3

y^{^{''}} + 4 y^{^{'}} + 3 y = 6 t e^{3 t}

y^{^{''}} - 9 y^{^{'}} + 14 y = 30 t - 34

What is the solution for y^{''}-36y=9e^{6x} ?
The solution for y^{''}-36y=9e^{6x} is y=c_{1}e^{6x}+c_{2}e^{-6x}+(3e^{6x}x)/4