What is the solution for y^{''}+8y^'+15y=0,y(0)=-2,y^'(0)=16 ?

The solution for y^{''}+8y^'+15y=0,y(0)=-2,y^'(0)=16 is y=3e^{-3t}-5e^{-5t}

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y^{''}+8y^'+15y=0,y(0)=-2,y^'(0)=16

y^{^{''}} + 8 y^{^{'}} + 15 y = 0, y (0) = - 2, y^{^{'}} (0) = 16

y = 3 e^{- 3 t} - 5 e^{- 5 t}

Solution steps

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

Solve linear ODE:

y = 3 e^{- 3 t} - 5 e^{- 5 t}

y = 3 e^{- 3 t} - 5 e^{- 5 t}

y^{^{''}} + 2 y^{^{'}} + 10 y = 0, y (0) = - 3, y^{^{'}} (0) = - 4

y^{^{''}} + 3 y = 0, y^{0} = 1, y^{^{'}} 0 = 3

\frac{1}{2} y^{^{''}} + 6 y^{^{'}} + 26 y = 0

y^{^{''}} - 9 y^{^{'}} = 0, y (0) = e^{3 x}

y^{^{''}} - 2 y^{^{'}} + 50 y = 0

What is the solution for y^{''}+8y^'+15y=0,y(0)=-2,y^'(0)=16 ?
The solution for y^{''}+8y^'+15y=0,y(0)=-2,y^'(0)=16 is y=3e^{-3t}-5e^{-5t}