What is the solution for y^{'''}+3y^{''}+y^'-5y=0 ?

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

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y^{'''}+3y^{''}+y^'-5y=0

y^{^{'''}} + 3 y^{^{''}} + y^{^{'}} - 5 y = 0

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

Solution steps

y^{'''} (t) + 3 y^{''} (t) + y^{'} (t) - 5 y = 0

Solve linear ODE:

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

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

\int 7 x^{6} d x

10 x e^{x}

\frac{d}{d x} (\frac{1}{18} (e^{9 x} + e^{- 9 x}))

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

f (x) = x^{2} + 8, (- 2, 12)

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