What is the solution for 25y^{''}+10y^'+y=0 ?

The solution for 25y^{''}+10y^'+y=0 is y=c_{1}e^{-t/5}+c_{2}e^{-t/5}t

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25y^{''}+10y^'+y=0

25 y^{^{''}} + 10 y^{^{'}} + y = 0

y = c_{1} e^{- \frac{t}{5}} + c_{2} e^{- \frac{t}{5}} t

Solution steps

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

Solve linear ODE:

y = c_{1} e^{- \frac{t}{5}} + c_{2} e^{- \frac{t}{5}} t

y = c_{1} e^{- \frac{t}{5}} + c_{2} e^{- \frac{t}{5}} t

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What is the solution for 25y^{''}+10y^'+y=0 ?
The solution for 25y^{''}+10y^'+y=0 is y=c_{1}e^{-t/5}+c_{2}e^{-t/5}t