What is the solution for x^{''''}-x^{''}=1 ?

The solution for x^{''''}-x^{''}=1 is x=c_{1}e^t+c_{2}e^{-t}+c_{3}+c_{4}t-(t^2)/2

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x^{''''}-x^{''}=1

x^{^{''''}} - x^{^{''}} = 1

x = c_{1} e^{t} + c_{2} e^{- t} + c_{3} + c_{4} t - \frac{t ^{2}}{2}

Solution steps

x^{(4)} (t) - x^{''} (t) = 1

Solve linear ODE:

x = c_{1} e^{t} + c_{2} e^{- t} + c_{3} + c_{4} t - \frac{t ^{2}}{2}

x = c_{1} e^{t} + c_{2} e^{- t} + c_{3} + c_{4} t - \frac{t ^{2}}{2}

y^{^{''}} - 2 y^{^{'}} + y = 3 e^{t}, y (0) = 1, y^{^{'}} (0) = 1

y^{^{''}} - 4 y^{^{'}} - 5 y = 125

y^{^{''}} + 4 y^{^{'}} + 5 y = - 5 x + 3 e^{- x}

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

y^{^{''}} + y^{^{'}} - 12 y = 2 cos (t), y (0) = 1, y^{^{'}} (0) = 1

What is the solution for x^{''''}-x^{''}=1 ?
The solution for x^{''''}-x^{''}=1 is x=c_{1}e^t+c_{2}e^{-t}+c_{3}+c_{4}t-(t^2)/2