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

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

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y^{'''}+y=0

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

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

Solution steps

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

Solve linear ODE:

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

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

x \to 9 lim (4 \cdot a + x)

x \to 5 - lim (\frac{x ^{2}}{x ^{2} + 6})

\int 9 \frac{x ^{3}}{x ^{7}} d x

\frac{d}{d x} (cos (arcsin (2 x)))

x^{2} - x - 4, - x^{2} + 3 x + 2

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