What is the solution for 9y^{''}+30y^'+25y=0,y(0)=a,y^'(0)=-1 ?

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

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9y^{''}+30y^'+25y=0,y(0)=a,y^'(0)=-1

9 y^{^{''}} + 30 y^{^{'}} + 25 y = 0, y (0) = a, y^{^{'}} (0) = - 1

y = a e^{- \frac{5 t}{3}} + (- 1 + \frac{5 a}{3}) e^{- \frac{5 t}{3}} t

Solution steps

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

Solve linear ODE:

y = a e^{- \frac{5 t}{3}} + (- 1 + \frac{5 a}{3}) e^{- \frac{5 t}{3}} t

y = a e^{- \frac{5 t}{3}} + (- 1 + \frac{5 a}{3}) e^{- \frac{5 t}{3}} t

\frac{\partial}{\partial r} (r cos (s))

y = x, y = \frac{1}{2} x, x = 16

\frac{d}{d x} ((x^{2} + 2)^{\frac{3}{2}})

y = 5 - x

4 x^{5} + 9

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