What is the solution for y^{''''}-y=e^x ?

The solution for y^{''''}-y=e^x is y=c_{1}e^x+c_{2}e^{-x}+c_{3}cos(x)+c_{4}sin(x)+(e^xx)/4

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

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

y = c_{1} e^{x} + c_{2} e^{- x} + c_{3} cos (x) + c_{4} sin (x) + \frac{e ^{x} x}{4}

Solution steps

y^{(4)} (x) - y = e^{x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- x} + c_{3} cos (x) + c_{4} sin (x) + \frac{e ^{x} x}{4}

y = c_{1} e^{x} + c_{2} e^{- x} + c_{3} cos (x) + c_{4} sin (x) + \frac{e ^{x} x}{4}

y^{^{''}} - 35 y^{^{'}} + 9 y = 60 t, y (0) = - 1, y^{^{'}} (0) = 2

y^{^{''}} + 2 y^{^{'}} + 5 y = 52 cos (3 x)

y^{^{''}} + 3 y^{^{'}} + 5 = 0

y^{^{''}} - 5 y^{^{'}} - 24 y = 5 + 2 t

y^{^{''}} - y^{^{'}} - 2 y = 3 t^{2} - 1

What is the solution for y^{''''}-y=e^x ?
The solution for y^{''''}-y=e^x is y=c_{1}e^x+c_{2}e^{-x}+c_{3}cos(x)+c_{4}sin(x)+(e^xx)/4