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

The solution for (d^2y)/(dx^2)-5(dy)/(dx)-24y=5+2x is y=c_{1}e^{8x}+c_{2}e^{-3x}-x/(12)-55/288

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

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

y = c_{1} e^{8 x} + c_{2} e^{- 3 x} - \frac{x}{12} - \frac{55}{288}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{8 x} + c_{2} e^{- 3 x} - \frac{x}{12} - \frac{55}{288}

y = c_{1} e^{8 x} + c_{2} e^{- 3 x} - \frac{x}{12} - \frac{55}{288}

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

\frac{1}{4} y^{^{''}} + 4 y = 2 tan (4 t) - \frac{1}{3} e^{2 t}

y^{^{''}} + 5 y^{^{'}} + 4 y = 1 + x + x^{2}

y^{^{''}} + y = - x^{2}, y (0) = 0, y (1) = 1

y^{^{''}} + y^{^{'}} - 2 y = u π (t) - u^{2} π (t)

What is the solution for (d^2y)/(dx^2)-5(dy)/(dx)-24y=5+2x ?
The solution for (d^2y)/(dx^2)-5(dy)/(dx)-24y=5+2x is y=c_{1}e^{8x}+c_{2}e^{-3x}-x/(12)-55/288