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

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

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

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

y = (5 + \frac{5}{3}) e^{- t} - \frac{5}{3} e^{- 4 t}

Solution steps

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

Solve linear ODE:

y = (5 + \frac{5}{3}) e^{- t} - \frac{5}{3} e^{- 4 t}

y = (5 + \frac{5}{3}) e^{- t} - \frac{5}{3} e^{- 4 t}

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

x^{^{''}} + x^{^{'}} + 5 x = 0

a x^{^{''}} + 2 x^{^{'}} = 0

y^{^{''}} + \frac{y ^{^{'}}}{2} - \frac{y}{2} = 0

\frac{d ^{3} y}{d x ^{3}} - 8 y = 0

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