What is the solution for y^{'''}-2y^{''}+8y^'=0 ?

The solution for y^{'''}-2y^{''}+8y^'=0 is y=c_{1}+e^t(c_{2}cos(sqrt(7)t)+c_{3}sin(sqrt(7)t))

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y^{'''}-2y^{''}+8y^'=0

y^{^{'''}} - 2 y^{^{''}} + 8 y^{^{'}} = 0

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

Solution steps

y^{'''} (t) - 2 y^{''} (t) + 8 y^{'} (t) = 0

Solve linear ODE:

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

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

What is the solution for y^{'''}-2y^{''}+8y^'=0 ?
The solution for y^{'''}-2y^{''}+8y^'=0 is y=c_{1}+e^t(c_{2}cos(sqrt(7)t)+c_{3}sin(sqrt(7)t))