What is the solution for 27y^{''}+(15-9sqrt(5))y^'-5sqrt(5)y=0 ?

The solution for 27y^{''}+(15-9sqrt(5))y^'-5sqrt(5)y=0 is y=c_{1}e^{(sqrt(5)t)/3}+c_{2}e^{-(5t)/9}

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27y^{''}+(15-9sqrt(5))y^'-5sqrt(5)y=0

27 y^{^{''}} + (15 - 95) y^{^{'}} - 55 y = 0

y = c_{1} e^{\frac{5 t}{3}} + c_{2} e^{- \frac{5 t}{9}}

Solution steps

27 y^{''} (t) + (15 - 95) y^{'} (t) - 55 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{5 t}{3}} + c_{2} e^{- \frac{5 t}{9}}

y = c_{1} e^{\frac{5 t}{3}} + c_{2} e^{- \frac{5 t}{9}}

324 y^{^{''}} - 612 y^{^{'}} + 289 y = 0, y (0) = 8, y^{^{'}} (0) = 5

y^{^{''}} - 13 y - 40 y = 0

25 y^{^{''}} + 10 y^{^{'}} + 5 y = 0

y^{^{''}} + 10 y^{^{'}} = 0, y (0) = - 2, y^{^{'}} (0) = - 2

- y^{^{''}} + 9 \cdot π^{2} y = 0

What is the solution for 27y^{''}+(15-9sqrt(5))y^'-5sqrt(5)y=0 ?
The solution for 27y^{''}+(15-9sqrt(5))y^'-5sqrt(5)y=0 is y=c_{1}e^{(sqrt(5)t)/3}+c_{2}e^{-(5t)/9}