What is the solution for 4y+9y^{''}=-12y^' ?

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

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4y+9y^{''}=-12y^'

4 y + 9 y^{^{''}} = - 12 y^{^{'}}

y = c_{1} e^{- \frac{2 t}{3}} + c_{2} e^{- \frac{2 t}{3}} t

Solution steps

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

Solve linear ODE:

y = c_{1} e^{- \frac{2 t}{3}} + c_{2} e^{- \frac{2 t}{3}} t

y = c_{1} e^{- \frac{2 t}{3}} + c_{2} e^{- \frac{2 t}{3}} t

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