What is the solution for y^{'''}+6y^{''}-37y^'-90y=0 ?

The solution for y^{'''}+6y^{''}-37y^'-90y=0 is y=c_{1}e^{-2t}+c_{2}e^{5t}+c_{3}e^{-9t}

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y^{'''}+6y^{''}-37y^'-90y=0

y^{^{'''}} + 6 y^{^{''}} - 37 y^{^{'}} - 90 y = 0

y = c_{1} e^{- 2 t} + c_{2} e^{5 t} + c_{3} e^{- 9 t}

Solution steps

y^{'''} (t) + 6 y^{''} (t) - 37 y^{'} (t) - 90 y = 0

Solve linear ODE:

y = c_{1} e^{- 2 t} + c_{2} e^{5 t} + c_{3} e^{- 9 t}

y = c_{1} e^{- 2 t} + c_{2} e^{5 t} + c_{3} e^{- 9 t}

9 y^{^{''}} + y = 0, y (0) = - 2, y^{^{'}} (0) = 1

u, \frac{d ^{2} u}{d x ^{2}} = a u (x)

y^{^{''}} - 7 y^{^{'}} + 8 y = 0, y (0) = 2, y^{^{'}} (0) = 7

y^{^{''}} + 3 y^{^{'}} - 18 y = 0, y (0) = 3, y^{^{'}} (0) = 18

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

What is the solution for y^{'''}+6y^{''}-37y^'-90y=0 ?
The solution for y^{'''}+6y^{''}-37y^'-90y=0 is y=c_{1}e^{-2t}+c_{2}e^{5t}+c_{3}e^{-9t}