What is the solution for 2y^{''}+13y^'+15y=0,y(0)=8,y^'(0)=-29.5 ?

The solution for 2y^{''}+13y^'+15y=0,y(0)=8,y^'(0)=-29.5 is y=3e^{-(3t)/2}+5e^{-5t}

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2y^{''}+13y^'+15y=0,y(0)=8,y^'(0)=-29.5

2 y^{^{''}} + 13 y^{^{'}} + 15 y = 0, y (0) = 8, y^{^{'}} (0) = - 29.5

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

Solution steps

2 y^{''} (t) + 13 y^{'} (t) + 15 y = 0

Solve linear ODE:

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

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

- 2 y^{^{'''}} - 4 y^{^{''}} + 10 y^{^{'}} + 12 y = 0

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

y^{^{''}} - 6 y^{^{'}} + 5 y = 0, y (0) = e^{x}

y^{^{''}} + 9 y^{^{'}} + 9 y = 0

y^{^{''}} - 9 y^{^{'}} + 81 y = 0

What is the solution for 2y^{''}+13y^'+15y=0,y(0)=8,y^'(0)=-29.5 ?
The solution for 2y^{''}+13y^'+15y=0,y(0)=8,y^'(0)=-29.5 is y=3e^{-(3t)/2}+5e^{-5t}