What is the solution for 25y^{''}+10y^'+y=0,y(0)=2,y^'(0)=1 ?

The solution for 25y^{''}+10y^'+y=0,y(0)=2,y^'(0)=1 is y=2e^{-t/5}+(7e^{-t/5}t)/5

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25y^{''}+10y^'+y=0,y(0)=2,y^'(0)=1

25 y^{^{''}} + 10 y^{^{'}} + y = 0, y (0) = 2, y^{^{'}} (0) = 1

y = 2 e^{- \frac{t}{5}} + \frac{7 e ^{- \frac{t}{5}} t}{5}

Solution steps

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

Solve linear ODE:

y = 2 e^{- \frac{t}{5}} + \frac{7 e ^{- \frac{t}{5}} t}{5}

y = 2 e^{- \frac{t}{5}} + \frac{7 e ^{- \frac{t}{5}} t}{5}

What is the solution for 25y^{''}+10y^'+y=0,y(0)=2,y^'(0)=1 ?
The solution for 25y^{''}+10y^'+y=0,y(0)=2,y^'(0)=1 is y=2e^{-t/5}+(7e^{-t/5}t)/5