What is the solution for (D^2+2)y=e^{x+2} ?

The solution for (D^2+2)y=e^{x+2} is y=c_{1}cos(sqrt(2)x)+c_{2}sin(sqrt(2)x)+(e^2)/3 e^x

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(D^2+2)y=e^{x+2}

(D^{2} + 2) y = e^{x + 2}

y = c_{1} cos (2 x) + c_{2} sin (2 x) + \frac{e ^{2}}{3} e^{x}

Solution steps

(D^{2} + 2) y = e^{x + 2}

Solve linear ODE:

y = c_{1} cos (2 x) + c_{2} sin (2 x) + \frac{e ^{2}}{3} e^{x}

y = c_{1} cos (2 x) + c_{2} sin (2 x) + \frac{e ^{2}}{3} e^{x}

(D^{2} - 4 D + 4) y = e^{x} + x^{2} + cos (2 x)

y^{^{''}} + 2 y^{^{'}} + 2 y = (t - π), y (0) = 2, y^{^{'}} (0) = 1

y^{^{''}} + 8 y^{^{'}} + 17 y = 2 e^{- 4 t} cos (t)

y^{^{''}} - 8 y^{^{'}} + 20 y = 100 x^{2} + 26 x e^{x}

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

What is the solution for (D^2+2)y=e^{x+2} ?
The solution for (D^2+2)y=e^{x+2} is y=c_{1}cos(sqrt(2)x)+c_{2}sin(sqrt(2)x)+(e^2)/3 e^x