What is the solution for y^{''}+12y^'+32y=0,y(0)=7,y^'(0)=-36 ?

The solution for y^{''}+12y^'+32y=0,y(0)=7,y^'(0)=-36 is y=5e^{-4t}+2e^{-8t}

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y^{''}+12y^'+32y=0,y(0)=7,y^'(0)=-36

y^{^{''}} + 12 y^{^{'}} + 32 y = 0, y (0) = 7, y^{^{'}} (0) = - 36

y = 5 e^{- 4 t} + 2 e^{- 8 t}

Solution steps

y^{''} (t) + 12 y^{'} (t) + 32 y = 0

Solve linear ODE:

y = 5 e^{- 4 t} + 2 e^{- 8 t}

y = 5 e^{- 4 t} + 2 e^{- 8 t}

What is the solution for y^{''}+12y^'+32y=0,y(0)=7,y^'(0)=-36 ?
The solution for y^{''}+12y^'+32y=0,y(0)=7,y^'(0)=-36 is y=5e^{-4t}+2e^{-8t}