What is the solution for y^{''}+2y=-e^3+e^{2x} ?

The solution for y^{''}+2y=-e^3+e^{2x} is y=c_{1}cos(sqrt(2)x)+c_{2}sin(sqrt(2)x)-(e^3)/2+1/6 e^{2x}

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

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

y = c_{1} cos (2 x) + c_{2} sin (2 x) - \frac{e ^{3}}{2} + \frac{1}{6} e^{2 x}

Solution steps

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

Solve linear ODE:

y = c_{1} cos (2 x) + c_{2} sin (2 x) - \frac{e ^{3}}{2} + \frac{1}{6} e^{2 x}

y = c_{1} cos (2 x) + c_{2} sin (2 x) - \frac{e ^{3}}{2} + \frac{1}{6} e^{2 x}

y^{^{''}} - 25 y = x e^{x}

y^{^{''}} + 4 y^{^{'}} + 4 y = 8 x

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

y^{^{''}} - y^{^{'}} - 6 y = - e^{x} + 12 x, y^{^{'}} (0) = - 2, y (0) = 1

2 x^{^{''}} + 5 x^{^{'}} + 2 x = 4 e^{- 2 t} - t

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