What is the solution for y^{'''}-y^{''}-24y^'-36y=0 ?

The solution for y^{'''}-y^{''}-24y^'-36y=0 is y=c_{1}e^{-2t}+c_{2}e^{-3t}+c_{3}e^{6t}

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y^{'''}-y^{''}-24y^'-36y=0

y^{^{'''}} - y^{^{''}} - 24 y^{^{'}} - 36 y = 0

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

Solution steps

y^{'''} (t) - y^{''} (t) - 24 y^{'} (t) - 36 y = 0

Solve linear ODE:

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

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

\frac{d ^{2} y}{d x ^{2}} + 225 y = 0

y^{^{'''}} - 27 y = 0, y (0) = - 1, y^{^{'}} (0) = 6, y^{^{'''}} (0) = 18

y^{^{'''}} - 8 y = 0, y (0) = 1, y^{^{'}} (0) = - 1, y^{^{''}} (0) = 0

x^{^{''}} + 42.1788 x^{^{'}} + 295.2064 x = 0

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

What is the solution for y^{'''}-y^{''}-24y^'-36y=0 ?
The solution for y^{'''}-y^{''}-24y^'-36y=0 is y=c_{1}e^{-2t}+c_{2}e^{-3t}+c_{3}e^{6t}