What is the solution for y^{'''}-7y^{''}-y^'+7y=0 ?

The solution for y^{'''}-7y^{''}-y^'+7y=0 is y=c_{1}e^{7t}+c_{2}e^{-t}+c_{3}e^t

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y^{'''}-7y^{''}-y^'+7y=0

y^{^{'''}} - 7 y^{^{''}} - y^{^{'}} + 7 y = 0

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

Solution steps

y^{'''} (t) - 7 y^{''} (t) - y^{'} (t) + 7 y = 0

Solve linear ODE:

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

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

What is the solution for y^{'''}-7y^{''}-y^'+7y=0 ?
The solution for y^{'''}-7y^{''}-y^'+7y=0 is y=c_{1}e^{7t}+c_{2}e^{-t}+c_{3}e^t