What is the solution for 9y^{''}+30y^'+25y=0 ?

The solution for 9y^{''}+30y^'+25y=0 is y=c_{1}e^{-(5t)/3}+c_{2}e^{-(5t)/3}t

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9y^{''}+30y^'+25y=0

9 y^{^{''}} + 30 y^{^{'}} + 25 y = 0

y = c_{1} e^{- \frac{5 t}{3}} + c_{2} e^{- \frac{5 t}{3}} t

Solution steps

9 y^{''} (t) + 30 y^{'} (t) + 25 y = 0

Solve linear ODE:

y = c_{1} e^{- \frac{5 t}{3}} + c_{2} e^{- \frac{5 t}{3}} t

y = c_{1} e^{- \frac{5 t}{3}} + c_{2} e^{- \frac{5 t}{3}} t

What is the solution for 9y^{''}+30y^'+25y=0 ?
The solution for 9y^{''}+30y^'+25y=0 is y=c_{1}e^{-(5t)/3}+c_{2}e^{-(5t)/3}t