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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

\frac{\partial}{\partial x} (2 x^{0.3} y^{0.3} + 1)

\int \frac{3 x ^{\frac{8}{3}}}{8} + C d x

\int arccot (5 x) d x

y^{^{'}} + \frac{2}{3} y = 1 - \frac{1}{2} t

\frac{d}{d x} (A (4 e^{2 x} x + 4 e^{2 x}))

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