What is the solution for y^{'''}-3y^{''}-46y^'-72y=0 ?

The solution for y^{'''}-3y^{''}-46y^'-72y=0 is y=c_{1}e^{-2t}+c_{2}e^{-4t}+c_{3}e^{9t}

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y^{'''}-3y^{''}-46y^'-72y=0

y^{^{'''}} - 3 y^{^{''}} - 46 y^{^{'}} - 72 y = 0

y = c_{1} e^{- 2 t} + c_{2} e^{- 4 t} + c_{3} e^{9 t}

Solution steps

y^{'''} (t) - 3 y^{''} (t) - 46 y^{'} (t) - 72 y = 0

Solve linear ODE:

y = c_{1} e^{- 2 t} + c_{2} e^{- 4 t} + c_{3} e^{9 t}

y = c_{1} e^{- 2 t} + c_{2} e^{- 4 t} + c_{3} e^{9 t}

y^{^{'''}} - y^{^{''}} - 100 y = 0

25 y^{^{''}} + 50 y^{^{'}} + 169 y = 0, y (0) = 4, y^{^{'}} (0) = 8

64 y^{^{''}} + 80 y^{^{'}} + 16 y = 0, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} + 4 y^{^{'}} + 13 y = 0, y (0) = 2, y^{^{'}} (0) = 5

y^{^{''}} + \frac{0}{3} y^{^{'}} + \frac{12}{3} y = 0

What is the solution for y^{'''}-3y^{''}-46y^'-72y=0 ?
The solution for y^{'''}-3y^{''}-46y^'-72y=0 is y=c_{1}e^{-2t}+c_{2}e^{-4t}+c_{3}e^{9t}