What is the solution for (d^2y)/(dx^2)+y=3+e^{-x}+5e^{2x} ?

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

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(d^2y)/(dx^2)+y=3+e^{-x}+5e^{2x}

\frac{d ^{2} y}{d x ^{2}} + y = 3 + e^{- x} + 5 e^{2 x}

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + y = 3 + e^{- x} + 5 e^{2 x}

Solve linear ODE:

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

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

y^{^{''}} + 20 y^{^{'}} + 200 y = 320

y^{^{'''}} - 2 y^{^{'}} + 4 y = sin (2 x)

y^{^{''}} + 9 y^{^{'}} + 14 y = 3 sin (2 x)

x^{^{''}} - x = e^{- t}

y^{^{''}} + 4 y^{^{'}} + 4 y = ln (x)

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