What is the solution for y^{''}+8y^'+15y=0,y(0)=0,y^'(0)=1 ?

The solution for y^{''}+8y^'+15y=0,y(0)=0,y^'(0)=1 is y= 1/2 e^{-3t}-1/2 e^{-5t}

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y^{''}+8y^'+15y=0,y(0)=0,y^'(0)=1

y^{^{''}} + 8 y^{^{'}} + 15 y = 0, y (0) = 0, y^{^{'}} (0) = 1

y = \frac{1}{2} e^{- 3 t} - \frac{1}{2} e^{- 5 t}

Solution steps

y^{''} (t) + 8 y^{'} (t) + 15 y = 0

Solve linear ODE:

y = \frac{1}{2} e^{- 3 t} - \frac{1}{2} e^{- 5 t}

y = \frac{1}{2} e^{- 3 t} - \frac{1}{2} e^{- 5 t}

What is the solution for y^{''}+8y^'+15y=0,y(0)=0,y^'(0)=1 ?
The solution for y^{''}+8y^'+15y=0,y(0)=0,y^'(0)=1 is y= 1/2 e^{-3t}-1/2 e^{-5t}