What is the solution for 9y^{''}-12y^'+4y=0,y(0)=2,y^'(0)=-2 ?

The solution for 9y^{''}-12y^'+4y=0,y(0)=2,y^'(0)=-2 is y=2e^{(2t)/3}-(10e^{(2t)/3}t)/(3)

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9y^{''}-12y^'+4y=0,y(0)=2,y^'(0)=-2

9 y^{^{''}} - 12 y^{^{'}} + 4 y = 0, y (0) = 2, y^{^{'}} (0) = - 2

y = 2 e^{\frac{2 t}{3}} - \frac{10 e ^{\frac{2 t}{3}} t}{3}

Solution steps

9 y^{''} (t) - 12 y^{'} (t) + 4 y = 0

Solve linear ODE:

y = 2 e^{\frac{2 t}{3}} - \frac{10 e ^{\frac{2 t}{3}} t}{3}

y = 2 e^{\frac{2 t}{3}} - \frac{10 e ^{\frac{2 t}{3}} t}{3}

y^{^{'''}} - 3 y^{^{''}} - 46 y^{^{'}} - 72 y = 0

y^{^{'''}} - y^{^{''}} - 100 y = 0

25 y^{^{''}} + 50 y^{^{'}} + 169 y = 0, y (0) = 4, y^{^{'}} (0) = 8

64 y^{^{''}} + 80 y^{^{'}} + 16 y = 0, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} + 4 y^{^{'}} + 13 y = 0, y (0) = 2, y^{^{'}} (0) = 5

What is the solution for 9y^{''}-12y^'+4y=0,y(0)=2,y^'(0)=-2 ?
The solution for 9y^{''}-12y^'+4y=0,y(0)=2,y^'(0)=-2 is y=2e^{(2t)/3}-(10e^{(2t)/3}t)/(3)