What is the solution for y^{''}+10y^'+9y=0,y(0)=2,y^'(0)=0 ?

The solution for y^{''}+10y^'+9y=0,y(0)=2,y^'(0)=0 is y=(2+1/4)e^{-t}-1/4 e^{-9t}

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y^{''}+10y^'+9y=0,y(0)=2,y^'(0)=0

y^{^{''}} + 10 y^{^{'}} + 9 y = 0, y (0) = 2, y^{^{'}} (0) = 0

y = (2 + \frac{1}{4}) e^{- t} - \frac{1}{4} e^{- 9 t}

Solution steps

y^{''} (t) + 10 y^{'} (t) + 9 y = 0

Solve linear ODE:

y = (2 + \frac{1}{4}) e^{- t} - \frac{1}{4} e^{- 9 t}

y = (2 + \frac{1}{4}) e^{- t} - \frac{1}{4} e^{- 9 t}

What is the solution for y^{''}+10y^'+9y=0,y(0)=2,y^'(0)=0 ?
The solution for y^{''}+10y^'+9y=0,y(0)=2,y^'(0)=0 is y=(2+1/4)e^{-t}-1/4 e^{-9t}