What is the solution for 2y^{''}+8y^'+y=0 ?

The solution for 2y^{''}+8y^'+y=0 is y=c_{1}e^{((-4+sqrt(14))t)/2}+c_{2}e^{-((4+sqrt(14))t)/2}

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2y^{''}+8y^'+y=0

2 y^{^{''}} + 8 y^{^{'}} + y = 0

y = c_{1} e^{\frac{( - 4 + 14 ) t}{2}} + c_{2} e^{- \frac{( 4 + 14 ) t}{2}}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{\frac{( - 4 + 14 ) t}{2}} + c_{2} e^{- \frac{( 4 + 14 ) t}{2}}

y = c_{1} e^{\frac{( - 4 + 14 ) t}{2}} + c_{2} e^{- \frac{( 4 + 14 ) t}{2}}

What is the solution for 2y^{''}+8y^'+y=0 ?
The solution for 2y^{''}+8y^'+y=0 is y=c_{1}e^{((-4+sqrt(14))t)/2}+c_{2}e^{-((4+sqrt(14))t)/2}