What is the solution for 625y^{''}-81y=0,y(0)=9,y^'(0)=6 ?

The solution for 625y^{''}-81y=0,y(0)=9,y^'(0)=6 is y=(9+23/6)e^{(9t)/(25)}-23/6 e^{-(9t)/(25)}

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625y^{''}-81y=0,y(0)=9,y^'(0)=6

625 y^{^{''}} - 81 y = 0, y (0) = 9, y^{^{'}} (0) = 6

y = (9 + \frac{23}{6}) e^{\frac{9 t}{25}} - \frac{23}{6} e^{- \frac{9 t}{25}}

Solution steps

625 y^{''} (t) - 81 y = 0

Solve linear ODE:

y = (9 + \frac{23}{6}) e^{\frac{9 t}{25}} - \frac{23}{6} e^{- \frac{9 t}{25}}

y = (9 + \frac{23}{6}) e^{\frac{9 t}{25}} - \frac{23}{6} e^{- \frac{9 t}{25}}

(D^{3} - D^{2} - 4 D + 4) y = 0

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

y^{^{''}} + 4 y^{^{'}} + 20 y = 0, y (0) = - 4, y^{^{'}} (0) = - 8

4 y^{^{''}} + 16 y^{^{'}} + \frac{1}{16} y = 0

y^{^{''}} + 5 y^{^{'}} + 6 y = 0, y (0) = 10, y^{^{'}} (0) = 0

What is the solution for 625y^{''}-81y=0,y(0)=9,y^'(0)=6 ?
The solution for 625y^{''}-81y=0,y(0)=9,y^'(0)=6 is y=(9+23/6)e^{(9t)/(25)}-23/6 e^{-(9t)/(25)}