What is the solution for 9y^{''}-4y=0 ?

The solution for 9y^{''}-4y=0 is y=c_{1}e^{(2t)/3}+c_{2}e^{-(2t)/3}

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9y^{''}-4y=0

9 y^{^{''}} - 4 y = 0

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

Solution steps

9 y^{''} (t) - 4 y = 0

Solve linear ODE:

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

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

y^{^{''}} - 6 y^{^{'}} + 90 y = 0

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 9 y = 0

y^{^{''}} + 20 y^{^{'}} + 100 y = 0

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (- 1) = 5

y^{^{''}} + 8 y^{^{'}} + 16 y = 0, y^{0} = 1, y^{^{'}} 0 = 0

What is the solution for 9y^{''}-4y=0 ?
The solution for 9y^{''}-4y=0 is y=c_{1}e^{(2t)/3}+c_{2}e^{-(2t)/3}