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

The solution for 9y^{''}-8y=0 is y=c_{1}e^{(2^{3/2}t)/3}+c_{2}e^{-(2^{3/2}t)/3}

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9y^{''}-8y=0

9 y^{^{''}} - 8 y = 0

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

Solution steps

9 y^{''} (t) - 8 y = 0

Solve linear ODE:

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

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

y^{^{''}} + 12 y^{^{'}} + 20 y = 0

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

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

y^{^{''}} + \frac{1}{10} y^{^{'}} = 0

y^{^{'''}} + 23 y^{^{''}} + 137 y^{^{'}} + 115 y = 0

What is the solution for 9y^{''}-8y=0 ?
The solution for 9y^{''}-8y=0 is y=c_{1}e^{(2^{3/2}t)/3}+c_{2}e^{-(2^{3/2}t)/3}