What is the solution for y^{'''}-2y^{''}-y^'+2y=e^{7t} ?

The solution for y^{'''}-2y^{''}-y^'+2y=e^{7t} is y=c_{1}e^{2t}+c_{2}e^{-t}+c_{3}e^t+1/240 e^{7t}

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y^{'''}-2y^{''}-y^'+2y=e^{7t}

y^{^{'''}} - 2 y^{^{''}} - y^{^{'}} + 2 y = e^{7 t}

y = c_{1} e^{2 t} + c_{2} e^{- t} + c_{3} e^{t} + \frac{1}{240} e^{7 t}

Solution steps

y^{'''} (t) - 2 y^{''} (t) - y^{'} (t) + 2 y = e^{7 t}

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} e^{- t} + c_{3} e^{t} + \frac{1}{240} e^{7 t}

y = c_{1} e^{2 t} + c_{2} e^{- t} + c_{3} e^{t} + \frac{1}{240} e^{7 t}

What is the solution for y^{'''}-2y^{''}-y^'+2y=e^{7t} ?
The solution for y^{'''}-2y^{''}-y^'+2y=e^{7t} is y=c_{1}e^{2t}+c_{2}e^{-t}+c_{3}e^t+1/240 e^{7t}