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

The solution for (d^2y)/(dx^2)+y=3e^{-5x} is y=c_{1}cos(x)+c_{2}sin(x)+3/26 e^{-5x}

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

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

y = c_{1} cos (x) + c_{2} sin (x) + \frac{3}{26} e^{- 5 x}

Solution steps

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

Solve linear ODE:

y = c_{1} cos (x) + c_{2} sin (x) + \frac{3}{26} e^{- 5 x}

y = c_{1} cos (x) + c_{2} sin (x) + \frac{3}{26} e^{- 5 x}

y^{^{''}} - 2 y^{^{'}} + 5 y = cos (2 x)

y^{^{''}} - 6 y^{^{'}} + 13 y = e^{3 x} cos (2 x)

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

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

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

What is the solution for (d^2y)/(dx^2)+y=3e^{-5x} ?
The solution for (d^2y)/(dx^2)+y=3e^{-5x} is y=c_{1}cos(x)+c_{2}sin(x)+3/26 e^{-5x}