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

The solution for y^{'''}-4y^{''}+9y^'=0 is y=c_{1}+e^{2t}(c_{2}cos(sqrt(5)t)+c_{3}sin(sqrt(5)t))

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

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

y = c_{1} + e^{2 t} (c_{2} cos (5 t) + c_{3} sin (5 t))

Solution steps

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

Solve linear ODE:

y = c_{1} + e^{2 t} (c_{2} cos (5 t) + c_{3} sin (5 t))

y = c_{1} + e^{2 t} (c_{2} cos (5 t) + c_{3} sin (5 t))

y^{^{''}} + 16 y = 0, y (\frac{π}{12}) = 4, y^{^{'}} (\frac{π}{12}) = - 8

y^{^{''}} - 7 y^{^{'}} - 8 y = 0

4 y^{^{''}} + 4 y^{^{'}} + 17 y = 0, y (0) = - 1, y^{^{'}} (0) = 2

81 y^{^{''}} + 18 y^{^{'}} + y = 0

16 y^{^{''''}} + 40 y^{^{''}} + 25 y = 0

What is the solution for y^{'''}-4y^{''}+9y^'=0 ?
The solution for y^{'''}-4y^{''}+9y^'=0 is y=c_{1}+e^{2t}(c_{2}cos(sqrt(5)t)+c_{3}sin(sqrt(5)t))