What is the solution for y^{''}+11y^'+24y=0,y(0)=1,y^'(0)=-11 ?

The solution for y^{''}+11y^'+24y=0,y(0)=1,y^'(0)=-11 is y=(1-8/5)e^{-3t}+8/5 e^{-8t}

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y^{''}+11y^'+24y=0,y(0)=1,y^'(0)=-11

y^{^{''}} + 11 y^{^{'}} + 24 y = 0, y (0) = 1, y^{^{'}} (0) = - 11

y = (1 - \frac{8}{5}) e^{- 3 t} + \frac{8}{5} e^{- 8 t}

Solution steps

y^{''} (t) + 11 y^{'} (t) + 24 y = 0

Solve linear ODE:

y = (1 - \frac{8}{5}) e^{- 3 t} + \frac{8}{5} e^{- 8 t}

y = (1 - \frac{8}{5}) e^{- 3 t} + \frac{8}{5} e^{- 8 t}

What is the solution for y^{''}+11y^'+24y=0,y(0)=1,y^'(0)=-11 ?
The solution for y^{''}+11y^'+24y=0,y(0)=1,y^'(0)=-11 is y=(1-8/5)e^{-3t}+8/5 e^{-8t}