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}+(5e^{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{5 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{5 e ^{\frac{t}{3}} t}{3}

y = e^{\frac{t}{3}} + \frac{5 e ^{\frac{t}{3}} t}{3}

2 y^{^{''}} + 12 y^{^{'}} + 19 y = 0, y (0) = 2, y^{^{'}} (0) = 0

y^{^{''}} + 32 y^{^{'}} + 160 y = 0

4 q^{^{''}} + 8 q^{^{'}} + \frac{1}{0.0125} q = 88 q

x^{^{''}} + 64 x = 0, x (0) = 0

y^{^{''}} - 256 y = 0

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}+(5e^{t/3}t)/3