What is the solution for y^{''}+8y^'+16y=0,y(0)=3,y^'(0)=-7 ?

The solution for y^{''}+8y^'+16y=0,y(0)=3,y^'(0)=-7 is y=3e^{-4t}+5te^{-4t}

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y^{''}+8y^'+16y=0,y(0)=3,y^'(0)=-7

y^{^{''}} + 8 y^{^{'}} + 16 y = 0, y (0) = 3, y^{^{'}} (0) = - 7

y = 3 e^{- 4 t} + 5 t e^{- 4 t}

Solution steps

y^{''} (t) + 8 y^{'} (t) + 16 y = 0

Solve linear ODE:

y = 3 e^{- 4 t} + 5 t e^{- 4 t}

y = 3 e^{- 4 t} + 5 t e^{- 4 t}

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What is the solution for y^{''}+8y^'+16y=0,y(0)=3,y^'(0)=-7 ?
The solution for y^{''}+8y^'+16y=0,y(0)=3,y^'(0)=-7 is y=3e^{-4t}+5te^{-4t}