What is the solution for y^{'''}+y^{''}+8y^'-10y=0 ?

The solution for y^{'''}+y^{''}+8y^'-10y=0 is y=c_{1}e^t+e^{-t}(c_{2}cos(3t)+c_{3}sin(3t))

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y^{'''}+y^{''}+8y^'-10y=0

y^{^{'''}} + y^{^{''}} + 8 y^{^{'}} - 10 y = 0

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

Solution steps

y^{'''} (t) + y^{''} (t) + 8 y^{'} (t) - 10 y = 0

Solve linear ODE:

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

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

What is the solution for y^{'''}+y^{''}+8y^'-10y=0 ?
The solution for y^{'''}+y^{''}+8y^'-10y=0 is y=c_{1}e^t+e^{-t}(c_{2}cos(3t)+c_{3}sin(3t))