What is the solution for (d^2y)/(dx^2)-16y=xe^x ?

The solution for (d^2y)/(dx^2)-16y=xe^x is y=c_{1}e^{4x}+c_{2}e^{-4x}-(e^xx)/(15)-2/225 e^x

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(d^2y)/(dx^2)-16y=xe^x

\frac{d ^{2} y}{d x ^{2}} - 16 y = x e^{x}

y = c_{1} e^{4 x} + c_{2} e^{- 4 x} - \frac{e ^{x} x}{15} - \frac{2}{225} e^{x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 16 y = x e^{x}

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{- 4 x} - \frac{e ^{x} x}{15} - \frac{2}{225} e^{x}

y = c_{1} e^{4 x} + c_{2} e^{- 4 x} - \frac{e ^{x} x}{15} - \frac{2}{225} e^{x}

y^{^{''}} + y = e^{- 2 π}, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} - 6 y^{^{'}} + 8 y = x^{3} - x + 1

y^{^{''}} - y = e^{2 t} + 4 t \cdot e^{2 t} + 8 t^{2} \cdot e^{t}

(d^{2} + 9) y = sec^{3} (x)

9 y^{^{''}} + 4 y = 3 x + 12 e - x, y (0) = 1, y^{^{'}} (0) = 0

What is the solution for (d^2y)/(dx^2)-16y=xe^x ?
The solution for (d^2y)/(dx^2)-16y=xe^x is y=c_{1}e^{4x}+c_{2}e^{-4x}-(e^xx)/(15)-2/225 e^x