What is the solution for (d^2y)/(dx^2)+(dy)/(dx)-20y=e^{-5x} ?

The solution for (d^2y)/(dx^2)+(dy)/(dx)-20y=e^{-5x} is y=c_{1}e^{4x}+c_{2}e^{-5x}-(e^{-5x}x)/9

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(d^2y)/(dx^2)+(dy)/(dx)-20y=e^{-5x}

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - 20 y = e^{- 5 x}

y = c_{1} e^{4 x} + c_{2} e^{- 5 x} - \frac{e ^{- 5 x} x}{9}

Solution steps

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - 20 y = e^{- 5 x}

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{- 5 x} - \frac{e ^{- 5 x} x}{9}

y = c_{1} e^{4 x} + c_{2} e^{- 5 x} - \frac{e ^{- 5 x} x}{9}

y^{^{''}} - y^{^{'}} - 16 = 0

y^{^{''}} + 40 y^{^{'}} + 6250 y = 100 cos (10 t)

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

y^{^{''}} - y^{^{'}} + 14 y = 4 + e^{\frac{x}{2}}

y^{^{''}} - 4 y = 32 t

What is the solution for (d^2y)/(dx^2)+(dy)/(dx)-20y=e^{-5x} ?
The solution for (d^2y)/(dx^2)+(dy)/(dx)-20y=e^{-5x} is y=c_{1}e^{4x}+c_{2}e^{-5x}-(e^{-5x}x)/9