What is the solution for (d^4y)/(dt^4)-y^{'''}-y^{''}+y^'=0 ?

The solution for (d^4y)/(dt^4)-y^{'''}-y^{''}+y^'=0 is y=c_{1}+c_{2}e^{-t}+c_{3}e^t+c_{4}te^t

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(d^4y)/(dt^4)-y^{'''}-y^{''}+y^'=0

\frac{d ^{4} y}{d t ^{4}} - y^{^{'''}} - y^{^{''}} + y^{^{'}} = 0

y = c_{1} + c_{2} e^{- t} + c_{3} e^{t} + c_{4} t e^{t}

Solution steps

y^{(4)} (t) - y^{'''} (t) - y^{''} (t) + y^{'} (t) = 0

Solve linear ODE:

y = c_{1} + c_{2} e^{- t} + c_{3} e^{t} + c_{4} t e^{t}

y = c_{1} + c_{2} e^{- t} + c_{3} e^{t} + c_{4} t e^{t}

y^{^{''}} + 5 y^{^{'}} + 4 y = 0, y (0) = 0, y^{^{'}} (0) = 0

2 u^{^{''}} + u^{^{'}} + 3 H (t) = 0

y^{^{''}} + 2 y^{^{'}} - 10 y = 0, y (0) = 2, y^{^{'}} (0) = - 1

2 y^{^{''}} - 0 y^{^{'}} + 18 y = 0

x^{^{''}} + 4 x^{^{'}} + 4 x = 0

What is the solution for (d^4y)/(dt^4)-y^{'''}-y^{''}+y^'=0 ?
The solution for (d^4y)/(dt^4)-y^{'''}-y^{''}+y^'=0 is y=c_{1}+c_{2}e^{-t}+c_{3}e^t+c_{4}te^t