What is the solution for y^{'''}-3y^{''}-4y^'+12y=0 ?

The solution for y^{'''}-3y^{''}-4y^'+12y=0 is y=c_{1}e^{3t}+c_{2}e^{-2t}+c_{3}e^{2t}

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y^{'''}-3y^{''}-4y^'+12y=0

y^{^{'''}} - 3 y^{^{''}} - 4 y^{^{'}} + 12 y = 0

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

Solution steps

y^{'''} (t) - 3 y^{''} (t) - 4 y^{'} (t) + 12 y = 0

Solve linear ODE:

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

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

What is the solution for y^{'''}-3y^{''}-4y^'+12y=0 ?
The solution for y^{'''}-3y^{''}-4y^'+12y=0 is y=c_{1}e^{3t}+c_{2}e^{-2t}+c_{3}e^{2t}