What is the solution for 9y^{''}-12y^'+11y=0 ?

The solution for 9y^{''}-12y^'+11y=0 is y=e^{(2t)/3}(c_{1}cos((sqrt(7)t)/3)+c_{2}sin((sqrt(7)t)/3))

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9y^{''}-12y^'+11y=0

9 y^{^{''}} - 12 y^{^{'}} + 11 y = 0

y = e^{\frac{2 t}{3}} (c_{1} cos (\frac{7 t}{3}) + c_{2} sin (\frac{7 t}{3}))

Solution steps

9 y^{''} (t) - 12 y^{'} (t) + 11 y = 0

Solve linear ODE:

y = e^{\frac{2 t}{3}} (c_{1} cos (\frac{7 t}{3}) + c_{2} sin (\frac{7 t}{3}))

y = e^{\frac{2 t}{3}} (c_{1} cos (\frac{7 t}{3}) + c_{2} sin (\frac{7 t}{3}))

y^{^{''}} + 12 y^{^{'}} + 36 y = 0, y (- 1) = 5, y^{^{'}} (- 1) = 3

4 y^{^{''}} - 19 y^{^{'}} + 12 y = 0, y (0) = 5, y^{^{'}} (0) = 13.5

y^{^{''}} = 6 y^{^{'}} - 8 y, y^{^{'}} (0) = 2

(d^{3} - d^{2} + d - 1) y = 0

\frac{d ^{2} y}{d x ^{2}} + 3 y = 0

What is the solution for 9y^{''}-12y^'+11y=0 ?
The solution for 9y^{''}-12y^'+11y=0 is y=e^{(2t)/3}(c_{1}cos((sqrt(7)t)/3)+c_{2}sin((sqrt(7)t)/3))