What is the solution for y^{''}+17y^'+72y=0 ?

The solution for y^{''}+17y^'+72y=0 is y=c_{1}e^{-8t}+c_{2}e^{-9t}

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y^{''}+17y^'+72y=0

y^{^{''}} + 17 y^{^{'}} + 72 y = 0

y = c_{1} e^{- 8 t} + c_{2} e^{- 9 t}

Solution steps

y^{''} (t) + 17 y^{'} (t) + 72 y = 0

Solve linear ODE:

y = c_{1} e^{- 8 t} + c_{2} e^{- 9 t}

y = c_{1} e^{- 8 t} + c_{2} e^{- 9 t}

y^{^{''}} + 2 y^{^{'}} + 17 y = 0, y (0) = 1, y^{^{'}} (0) = - 1

y^{^{''}} - 11 y^{^{'}} + 24 y = 0

16 y^{^{''''}} + 16 y^{^{''}} + 4 y = 0

x^{^{''}} + 64 x = 0

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

What is the solution for y^{''}+17y^'+72y=0 ?
The solution for y^{''}+17y^'+72y=0 is y=c_{1}e^{-8t}+c_{2}e^{-9t}