What is the solution for y^{'''}+2y^{''}-63y^'=0 ?

The solution for y^{'''}+2y^{''}-63y^'=0 is y=c_{1}+c_{2}e^{7t}+c_{3}e^{-9t}

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y^{'''}+2y^{''}-63y^'=0

y^{^{'''}} + 2 y^{^{''}} - 63 y^{^{'}} = 0

y = c_{1} + c_{2} e^{7 t} + c_{3} e^{- 9 t}

Solution steps

y^{'''} (t) + 2 y^{''} (t) - 63 y^{'} (t) = 0

Solve linear ODE:

y = c_{1} + c_{2} e^{7 t} + c_{3} e^{- 9 t}

y = c_{1} + c_{2} e^{7 t} + c_{3} e^{- 9 t}

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

0.05 q^{^{''}} + 2 q^{^{'}} + \frac{1}{0.01} q = 0

x^{^{''}} + 6 x^{^{'}} + 25 x = 0, x (0) = 3, x^{^{'}} (0) = 8

\frac{d ^{2} y}{d x ^{2}} = k y

y^{^{''}} - 12 y^{^{'}} + 20 y = 0

What is the solution for y^{'''}+2y^{''}-63y^'=0 ?
The solution for y^{'''}+2y^{''}-63y^'=0 is y=c_{1}+c_{2}e^{7t}+c_{3}e^{-9t}