# Thread: Equilibrium solutions to a D.E

1. ## Equilibrium solutions to a D.E

hey all,

How can I find remaining equilibrium solutions to $\displaystyle \frac{dy}{dt} = -sin(x) + \frac{x}{2}$ ? The only solution I can find is 0.

I see that it also touches the t-axis at approx -1.8 and 1.8, I guess I will just have to rely on the approximated values.

2. Originally Posted by Oiler
hey all,

How can I find remaining equilibrium solutions to $\displaystyle \frac{dy}{dt} = -sin(x) + \frac{x}{2}$ ? The only solution I can find is 0.
Are the x's meant to be y's ....? Are there boundary conditions? Note that by inspection sin(y) = y/2 for y = 0 but the other solutions cannot be found in closed form using algebra: solve Sin&#91;x&#93; &#61; x&#47;2 - Wolfram|Alpha

3. Originally Posted by Oiler
hey all,

How can I find remaining equilibrium solutions to $\displaystyle \frac{dy}{dt} = -sin(x) + \frac{x}{2}$ ? The only solution I can find is 0.

I see that it also touches the t-axis at approx -1.8 and 1.8, I guess I will just have to rely on the approximated values.
There are actually three equilibrium points. x = 0 and x = +/- 1.562161 for y = const. See here.

-Dan

Aww! Beaten out by Elastic Man!