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

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

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

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

y = - \frac{e ^{- \frac{2 t}{3}} ( - 3 - 3 c _{2} )}{2} + c_{2} e^{- \frac{2 t}{3}} t

Solution steps

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

Solve linear ODE:

y = - \frac{e ^{- \frac{2 t}{3}} ( - 3 - 3 c _{2} )}{2} + c_{2} e^{- \frac{2 t}{3}} t

y = - \frac{e ^{- \frac{2 t}{3}} ( - 3 - 3 c _{2} )}{2} + c_{2} e^{- \frac{2 t}{3}} t

y^{^{''}} - 5 y^{^{'}} = 0, y (0) = 7 - 7 e^{5}, y (1) = 0

y^{^{''}} + 12 y^{^{'}} + a y = 0

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

\frac{d ^{2} y}{d x ^{2}} + 5^{2} y = 0

y^{^{''}} + 6 y^{^{'}} + 13 y = 0, y (0) = 3

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