What is the solution for y^{'''}+y^{''}-4y^'-4y=0 ?

The solution for y^{'''}+y^{''}-4y^'-4y=0 is y=c_{1}e^{-t}+c_{2}e^{-2t}+c_{3}e^{2t}

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y^{'''}+y^{''}-4y^'-4y=0

y^{^{'''}} + y^{^{''}} - 4 y^{^{'}} - 4 y = 0

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

Solution steps

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

Solve linear ODE:

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

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

What is the solution for y^{'''}+y^{''}-4y^'-4y=0 ?
The solution for y^{'''}+y^{''}-4y^'-4y=0 is y=c_{1}e^{-t}+c_{2}e^{-2t}+c_{3}e^{2t}