What is the solution for y^{'''}-2y^{''}-21y^'-18y=0 ?

The solution for y^{'''}-2y^{''}-21y^'-18y=0 is y=c_{1}e^{-t}+c_{2}e^{-3t}+c_{3}e^{6t}

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y^{'''}-2y^{''}-21y^'-18y=0

y^{^{'''}} - 2 y^{^{''}} - 21 y^{^{'}} - 18 y = 0

y = c_{1} e^{- t} + c_{2} e^{- 3 t} + c_{3} e^{6 t}

Solution steps

y^{'''} (t) - 2 y^{''} (t) - 21 y^{'} (t) - 18 y = 0

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} e^{- 3 t} + c_{3} e^{6 t}

y = c_{1} e^{- t} + c_{2} e^{- 3 t} + c_{3} e^{6 t}

4 x^{^{''}} + 8 x^{^{'}} + 4 x = 0

\frac{d ^{4} y}{d x ^{4}} - 16 y = 0

y^{^{''}} - 6 y^{^{'}} = 0, y (0) = 4 - 4 e^{6}, y (1) = 0

y^{^{'''}} - y^{^{''}} - 12 y^{^{'}} = 0

x^{^{''}} + 4 k^{2} x = 0

What is the solution for y^{'''}-2y^{''}-21y^'-18y=0 ?
The solution for y^{'''}-2y^{''}-21y^'-18y=0 is y=c_{1}e^{-t}+c_{2}e^{-3t}+c_{3}e^{6t}