What is the solution for y^{''}+8y^'+16y=0,y(0)=5,y^'(0)=23 ?

The solution for y^{''}+8y^'+16y=0,y(0)=5,y^'(0)=23 is y=5e^{-4t}+43te^{-4t}

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y^{''}+8y^'+16y=0,y(0)=5,y^'(0)=23

y^{^{''}} + 8 y^{^{'}} + 16 y = 0, y (0) = 5, y^{^{'}} (0) = 23

y = 5 e^{- 4 t} + 43 t e^{- 4 t}

Solution steps

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

Solve linear ODE:

y = 5 e^{- 4 t} + 43 t e^{- 4 t}

y = 5 e^{- 4 t} + 43 t e^{- 4 t}

2 y^{^{''}} - 13 y^{^{'}} + 20 y = 0, y (0) = - 2, y^{^{'}} (0) = - 11

4 y^{^{''}} + 20 y^{^{'}} + 29 y = 0, y (1) = 8

y^{^{''}} - 3 y^{^{'}} + α y = 0, y (0) = 1, y^{^{'}} (0) = 5

y^{^{''}} + 2 \cdot y^{^{'}} + 4 \cdot y = 0

y^{^{'''''}} + 4 y^{^{''''}} - 8 y^{^{'''}} - 4 y^{^{''}} = 0

What is the solution for y^{''}+8y^'+16y=0,y(0)=5,y^'(0)=23 ?
The solution for y^{''}+8y^'+16y=0,y(0)=5,y^'(0)=23 is y=5e^{-4t}+43te^{-4t}