What is the solution for 2y^{''}+10y^'+8y=0,y^'(0)=0,y(0)=5 ?

The solution for 2y^{''}+10y^'+8y=0,y^'(0)=0,y(0)=5 is y= 20/3 e^{-t}-5/3 e^{-4t}

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2y^{''}+10y^'+8y=0,y^'(0)=0,y(0)=5

2 y^{^{''}} + 10 y^{^{'}} + 8 y = 0, y^{^{'}} (0) = 0, y (0) = 5

y = \frac{20}{3} e^{- t} - \frac{5}{3} e^{- 4 t}

Solution steps

2 y^{''} (t) + 10 y^{'} (t) + 8 y = 0

Solve linear ODE:

y = \frac{20}{3} e^{- t} - \frac{5}{3} e^{- 4 t}

y = \frac{20}{3} e^{- t} - \frac{5}{3} e^{- 4 t}

2 y^{^{''}} - 4 y^{^{'}} + 5 y = 0

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} - 63 y = 0

25 y^{^{''}} + 80 y^{^{'}} + 64 y = 0, y (0) = 8

y^{^{''}} - 12 y^{^{'}} + 36 y = 0, y (0) = 9, y^{^{'}} (0) = 5

7 y^{^{''}} - 8 y^{^{'}} + y = 0, y (0) = 7, y^{^{'}} (0) = \frac{1}{7}

What is the solution for 2y^{''}+10y^'+8y=0,y^'(0)=0,y(0)=5 ?
The solution for 2y^{''}+10y^'+8y=0,y^'(0)=0,y(0)=5 is y= 20/3 e^{-t}-5/3 e^{-4t}