What is the solution for (d^2y)/(dx^2)+4(dy)/(dx)-5y=24e^x ?

The solution for (d^2y)/(dx^2)+4(dy)/(dx)-5y=24e^x is y=c_{1}e^x+c_{2}e^{-5x}+4xe^x

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(d^2y)/(dx^2)+4(dy)/(dx)-5y=24e^x

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} - 5 y = 24 e^{x}

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} - 5 y = 24 e^{x}

Solve linear ODE:

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

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

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 3 y = 6 x^{2} + 19 x + 5

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

(D^{4} - 8 D^{2} + 16) y = x e^{2 x}

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

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

What is the solution for (d^2y)/(dx^2)+4(dy)/(dx)-5y=24e^x ?
The solution for (d^2y)/(dx^2)+4(dy)/(dx)-5y=24e^x is y=c_{1}e^x+c_{2}e^{-5x}+4xe^x