What is the solution for 9y^{''}+6y^'+y=0,y(0)=1,y^'(0)=2 ?

The solution for 9y^{''}+6y^'+y=0,y(0)=1,y^'(0)=2 is y=e^{-t/3}+(7e^{-t/3}t)/3

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9y^{''}+6y^'+y=0,y(0)=1,y^'(0)=2

9 y^{^{''}} + 6 y^{^{'}} + y = 0, y (0) = 1, y^{^{'}} (0) = 2

y = e^{- \frac{t}{3}} + \frac{7 e ^{- \frac{t}{3}} t}{3}

Solution steps

9 y^{''} (t) + 6 y^{'} (t) + y = 0

Solve linear ODE:

y = e^{- \frac{t}{3}} + \frac{7 e ^{- \frac{t}{3}} t}{3}

y = e^{- \frac{t}{3}} + \frac{7 e ^{- \frac{t}{3}} t}{3}

What is the solution for 9y^{''}+6y^'+y=0,y(0)=1,y^'(0)=2 ?
The solution for 9y^{''}+6y^'+y=0,y(0)=1,y^'(0)=2 is y=e^{-t/3}+(7e^{-t/3}t)/3