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

2 y^{^{''}} + 2 y^{^{'}} + 8 y = 0, y (0) = 5, y^{^{'}} (0) = 0

y^{^{''}} - 2 y^{^{'}} + y = 0, y (0) = 1, y^{^{'}} (0) = 3

y^{^{'}} = 4 y^{^{''}}

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (0) = 1, y^{^{'}} (0) = - 5

y^{^{''}} + 2 y^{^{'}} + 10 y = 0, y (0) = 3, y^{^{'}} (0) = - 2

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