What is the solution for y^{''}-1/9 y=0 ?

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

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y^{''}-1/9 y=0

y^{^{''}} - \frac{1}{9} y = 0

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

Solution steps

y^{''} (t) - \frac{1}{9} y = 0

Solve linear ODE:

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

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

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

77 y^{^{''''}} + 156 y^{^{''}} + 64 y = 0

y^{^{''}} + 13 y^{^{'}} + 42 y = 0, y (0) = 8, y^{^{'}} (0) = - 51

y^{^{''}} + 4 y^{^{'}} + 5 y = 0, y (\frac{π}{2}) = 0, y^{^{'}} (\frac{π}{2}) = 2

y^{^{''}} + 4 y^{^{'}} + 5 y = 0, y (\frac{π}{2}) = 0, y^{^{'}} (\frac{π}{2}) = 9

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