What is the solution for 9y^{''}-12y^'+4y=0,y(0)=4,y^'(0)=-1 ?

The solution for 9y^{''}-12y^'+4y=0,y(0)=4,y^'(0)=-1 is y=4e^{(2t)/3}-(11e^{(2t)/3}t)/(3)

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9y^{''}-12y^'+4y=0,y(0)=4,y^'(0)=-1

9 y^{^{''}} - 12 y^{^{'}} + 4 y = 0, y (0) = 4, y^{^{'}} (0) = - 1

y = 4 e^{\frac{2 t}{3}} - \frac{11 e ^{\frac{2 t}{3}} t}{3}

Solution steps

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

Solve linear ODE:

y = 4 e^{\frac{2 t}{3}} - \frac{11 e ^{\frac{2 t}{3}} t}{3}

y = 4 e^{\frac{2 t}{3}} - \frac{11 e ^{\frac{2 t}{3}} t}{3}

y^{^{''}} - 25 y^{^{'}} + 144 y = 0

x^{^{''}} + 3 x^{^{'}} + x = 0

y^{^{''}} + 16 y^{^{'}} + 100 y = 0

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

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

What is the solution for 9y^{''}-12y^'+4y=0,y(0)=4,y^'(0)=-1 ?
The solution for 9y^{''}-12y^'+4y=0,y(0)=4,y^'(0)=-1 is y=4e^{(2t)/3}-(11e^{(2t)/3}t)/(3)