What is the solution for 81y^{''}-90y^'+106y=0 ?

The solution for 81y^{''}-90y^'+106y=0 is y=e^{(5t)/9}(c_{1}cos(t)+c_{2}sin(t))

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81y^{''}-90y^'+106y=0

81 y^{^{''}} - 90 y^{^{'}} + 106 y = 0

y = e^{\frac{5 t}{9}} (c_{1} cos (t) + c_{2} sin (t))

Solution steps

81 y^{''} (t) - 90 y^{'} (t) + 106 y = 0

Solve linear ODE:

y = e^{\frac{5 t}{9}} (c_{1} cos (t) + c_{2} sin (t))

y = e^{\frac{5 t}{9}} (c_{1} cos (t) + c_{2} sin (t))

y^{^{''}} + 4 y^{^{'}} + 13 y = 0, y (0) = 4, y^{^{'}} (0) = - 7

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

y^{^{''}} + 14 y^{^{'}} + 51 y = 0

y^{^{'''}} - 4 y^{^{''}} - 5 y^{^{'}} = 0, y (1) = 0, y^{^{'}} (1) = 8

y^{^{''}} - 1 y^{^{'}} + 0.1 y = 0

What is the solution for 81y^{''}-90y^'+106y=0 ?
The solution for 81y^{''}-90y^'+106y=0 is y=e^{(5t)/9}(c_{1}cos(t)+c_{2}sin(t))