What is the solution for y^{'''}-6y^{''}+11y^'=0 ?

The solution for y^{'''}-6y^{''}+11y^'=0 is y=c_{1}+e^{3t}(c_{2}cos(sqrt(2)t)+c_{3}sin(sqrt(2)t))

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y^{'''}-6y^{''}+11y^'=0

y^{^{'''}} - 6 y^{^{''}} + 11 y^{^{'}} = 0

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

Solution steps

y^{'''} (t) - 6 y^{''} (t) + 11 y^{'} (t) = 0

Solve linear ODE:

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

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

81 y^{^{''}} - 234 y^{^{'}} + 169 y = 0

y^{^{''}} + 806 y^{^{'}} + 8000 y = 0

(d^{2} + 4 d + 4) y = 0

y^{^{'''}} - 15 y^{^{''}} + 66 y^{^{'}} - 80 y = 0

y^{^{''}} - 6 y^{^{'}} + 5 y = 0, y (0) = 5, y^{^{'}} (0) = - 6

What is the solution for y^{'''}-6y^{''}+11y^'=0 ?
The solution for y^{'''}-6y^{''}+11y^'=0 is y=c_{1}+e^{3t}(c_{2}cos(sqrt(2)t)+c_{3}sin(sqrt(2)t))