What is the solution for y^{'''}-5y^{''}+y^'-5y=0 ?

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

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y^{'''}-5y^{''}+y^'-5y=0

y^{^{'''}} - 5 y^{^{''}} + y^{^{'}} - 5 y = 0

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

Solution steps

y^{'''} (t) - 5 y^{''} (t) + y^{'} (t) - 5 y = 0

Solve linear ODE:

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

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

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