What is the solution for (d^2y)/(dx^2)-9y=e^x(1+x) ?

The solution for (d^2y)/(dx^2)-9y=e^x(1+x) is y=c_{1}e^{3x}+c_{2}e^{-3x}-(e^xx)/8-5/32 e^x

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(d^2y)/(dx^2)-9y=e^x(1+x)

\frac{d ^{2} y}{d x ^{2}} - 9 y = e^{x} (1 + x)

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{e ^{x} x}{8} - \frac{5}{32} e^{x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 9 y = e^{x} (1 + x)

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{e ^{x} x}{8} - \frac{5}{32} e^{x}

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{e ^{x} x}{8} - \frac{5}{32} e^{x}

y^{^{''}} - 6 y^{^{'}} + 9 y = 15 x + 6

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

y^{^{''}} + 81 y = 2 sin (x)

y^{^{''}} + 8 y^{^{'}} + \frac{1}{2} y = 10 sin (4 x)

y^{^{'''}} - 4 y^{^{''}} + 5 y^{^{'}} - 2 y = 6 \cdot e^{x} + 10 cos (x)

What is the solution for (d^2y)/(dx^2)-9y=e^x(1+x) ?
The solution for (d^2y)/(dx^2)-9y=e^x(1+x) is y=c_{1}e^{3x}+c_{2}e^{-3x}-(e^xx)/8-5/32 e^x