What is the solution for y^{''}+5y^'+4y=0,y(0)=0,y^'(0)=1 ?

The solution for y^{''}+5y^'+4y=0,y(0)=0,y^'(0)=1 is y= 1/3 e^{-t}-1/3 e^{-4t}

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y^{''}+5y^'+4y=0,y(0)=0,y^'(0)=1

y^{^{''}} + 5 y^{^{'}} + 4 y = 0, y (0) = 0, y^{^{'}} (0) = 1

y = \frac{1}{3} e^{- t} - \frac{1}{3} e^{- 4 t}

Solution steps

y^{''} (t) + 5 y^{'} (t) + 4 y = 0

Solve linear ODE:

y = \frac{1}{3} e^{- t} - \frac{1}{3} e^{- 4 t}

y = \frac{1}{3} e^{- t} - \frac{1}{3} e^{- 4 t}

What is the solution for y^{''}+5y^'+4y=0,y(0)=0,y^'(0)=1 ?
The solution for y^{''}+5y^'+4y=0,y(0)=0,y^'(0)=1 is y= 1/3 e^{-t}-1/3 e^{-4t}