What is the solution for 2500y^{''}-9y=0,y(0)=6,y^'(0)=7 ?

The solution for 2500y^{''}-9y=0,y(0)=6,y^'(0)=7 is y=(6+166/3)e^{(3t)/(50)}-166/3 e^{-(3t)/(50)}

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2500y^{''}-9y=0,y(0)=6,y^'(0)=7

2500 y^{^{''}} - 9 y = 0, y (0) = 6, y^{^{'}} (0) = 7

y = (6 + \frac{166}{3}) e^{\frac{3 t}{50}} - \frac{166}{3} e^{- \frac{3 t}{50}}

Solution steps

2500 y^{''} (t) - 9 y = 0

Solve linear ODE:

y = (6 + \frac{166}{3}) e^{\frac{3 t}{50}} - \frac{166}{3} e^{- \frac{3 t}{50}}

y = (6 + \frac{166}{3}) e^{\frac{3 t}{50}} - \frac{166}{3} e^{- \frac{3 t}{50}}

\frac{d ^{3} x}{d t ^{3}} - x = 0

16 y^{^{''}} - 72 y^{^{'}} + 81 y = 0, y^{^{'}} (0) = 8

x^{^{''}} + 16 x = 0, x^{^{'}} (0) = 5

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

y^{^{''''}} - 6 y^{^{'''}} + 17 y^{^{''}} - 28 y^{^{'}} + 20 y = 0

What is the solution for 2500y^{''}-9y=0,y(0)=6,y^'(0)=7 ?
The solution for 2500y^{''}-9y=0,y(0)=6,y^'(0)=7 is y=(6+166/3)e^{(3t)/(50)}-166/3 e^{-(3t)/(50)}