What is the solution for y^{''}+2/3 y^'+1/9 y=0 ?

The solution for y^{''}+2/3 y^'+1/9 y=0 is y=c_{1}e^{-t/3}+c_{2}e^{-t/3}t

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y^{''}+2/3 y^'+1/9 y=0

y^{^{''}} + \frac{2}{3} y^{^{'}} + \frac{1}{9} y = 0

y = c_{1} e^{- \frac{t}{3}} + c_{2} e^{- \frac{t}{3}} t

Solution steps

y^{''} (t) + \frac{2}{3} y^{'} (t) + \frac{1}{9} y = 0

Solve linear ODE:

y = c_{1} e^{- \frac{t}{3}} + c_{2} e^{- \frac{t}{3}} t

y = c_{1} e^{- \frac{t}{3}} + c_{2} e^{- \frac{t}{3}} t

What is the solution for y^{''}+2/3 y^'+1/9 y=0 ?
The solution for y^{''}+2/3 y^'+1/9 y=0 is y=c_{1}e^{-t/3}+c_{2}e^{-t/3}t