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}

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