What is the solution for (d^3x)/(dt^3)+(dx)/(dt)=0 ?

The solution for (d^3x)/(dt^3)+(dx)/(dt)=0 is x=c_{1}+c_{2}cos(t)+c_{3}sin(t)

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(d^3x)/(dt^3)+(dx)/(dt)=0

\frac{d ^{3} x}{d t ^{3}} + \frac{d x}{d t} = 0

x = c_{1} + c_{2} cos (t) + c_{3} sin (t)

Solution steps

\frac{d ^{3} x}{d t ^{3}} + \frac{d x}{d t} = 0

Solve linear ODE:

x = c_{1} + c_{2} cos (t) + c_{3} sin (t)

x = c_{1} + c_{2} cos (t) + c_{3} sin (t)

100 y^{^{''}} - y = 0, y (- 8) = 1, y^{^{'}} (- 8) = - 1

49 y^{^{''}} - 4 y = 0

x^{^{''}} + \frac{9.81}{0.32} x = 0, x (0) = - 8, x^{^{'}} (0) = 5

4 y^{^{''}} - y^{^{'}} - 3 y = 0, y (0) = 5, y^{^{'}} (0) = 0

y^{^{''''}} - 7 y^{^{'''}} + 12 y^{^{''}} = 0

What is the solution for (d^3x)/(dt^3)+(dx)/(dt)=0 ?
The solution for (d^3x)/(dt^3)+(dx)/(dt)=0 is x=c_{1}+c_{2}cos(t)+c_{3}sin(t)