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

The solution for y^{''}+y=-e^3+e^{2x} is y=c_{1}cos(x)+c_{2}sin(x)-e^3+1/5 e^{2x}

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

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

y = c_{1} cos (x) + c_{2} sin (x) - e^{3} + \frac{1}{5} e^{2 x}

Solution steps

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

Solve linear ODE:

y = c_{1} cos (x) + c_{2} sin (x) - e^{3} + \frac{1}{5} e^{2 x}

y = c_{1} cos (x) + c_{2} sin (x) - e^{3} + \frac{1}{5} e^{2 x}

y^{^{''}} - 4 y^{^{'}} + 4 y = 5 t^{2}

\frac{d ^{2} y}{d x ^{2}} - 16 \frac{d y}{d x} + 64 y = (x + 1) e^{x}

y^{^{''}} - 5 y^{^{'}} + 2 y = x e^{x}

y^{^{''}} + 3 y^{^{'}} - 4 y = 3 e^{x}

y^{^{''}} - y^{^{'}} + y = 12 sin (t) - 4 e^{2 t}

What is the solution for y^{''}+y=-e^3+e^{2x} ?
The solution for y^{''}+y=-e^3+e^{2x} is y=c_{1}cos(x)+c_{2}sin(x)-e^3+1/5 e^{2x}