What is the solution for 625y^{''}-9y=0,y(0)=9,y^'(0)=8 ?

The solution for 625y^{''}-9y=0,y(0)=9,y^'(0)=8 is y=(9+173/6)e^{(3t)/(25)}-173/6 e^{-(3t)/(25)}

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625y^{''}-9y=0,y(0)=9,y^'(0)=8

625 y^{^{''}} - 9 y = 0, y (0) = 9, y^{^{'}} (0) = 8

y = (9 + \frac{173}{6}) e^{\frac{3 t}{25}} - \frac{173}{6} e^{- \frac{3 t}{25}}

Solution steps

625 y^{''} (t) - 9 y = 0

Solve linear ODE:

y = (9 + \frac{173}{6}) e^{\frac{3 t}{25}} - \frac{173}{6} e^{- \frac{3 t}{25}}

y = (9 + \frac{173}{6}) e^{\frac{3 t}{25}} - \frac{173}{6} e^{- \frac{3 t}{25}}

\frac{5}{8} \frac{d ^{2} x}{d t ^{2}} + 40 x = 0

y^{^{''''}} - 12 y^{^{''}} + 36 y = 0

y^{^{''}} + 1 y^{^{'}} + 0 y = 0

y^{^{''}} + k (1 + k) y = 0

y^{^{''}} + y^{^{'}} - 30 y = 0, y (0) = 1, y^{^{'}} (0) = 38

What is the solution for 625y^{''}-9y=0,y(0)=9,y^'(0)=8 ?
The solution for 625y^{''}-9y=0,y(0)=9,y^'(0)=8 is y=(9+173/6)e^{(3t)/(25)}-173/6 e^{-(3t)/(25)}