## Solving Differential - Equation of Motion

Let's say I have the equation:

##\ddot {\theta}(t)(J + y(t)^2) + 2 \dot {\theta}(t) y(t) \dot y(t) + \ddot y(t)Jn##

It's the general form of an equation I'm working with to describe the motion of a beam. As you can see both ##{\theta}(t)## and y(t) are equations of t. J and Jn are just constants.

I'm wanting to solve for ##{\theta}(t)##, ##\dot {\theta}(t)##, and ##\ddot {\theta}(t)## as a function of time. These will correspond to position, velocity, and acceleration around an axis.

##{\theta}(t)## = (equation of t)

Any help would be greatly appreciated!

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 have you tried using e^iat style functions for theta(t)? I ask because its sometimes used when you periodic motion which in your case is rotating about an axis.
 Recognitions: Gold Member Science Advisor Staff Emeritus That's not a differential equation. Is one of those "+" signs supposed to be an "=" sign? Or is the whole formula equal to something, say "0"?

## Solving Differential - Equation of Motion

 Quote by HallsofIvy That's not a differential equation. Is one of those "+" signs supposed to be an "=" sign? Or is the whole formula equal to something, say "0"?
Terribly sorry about that, you are correct. All of that is equal to 0.

As for the other response, I thought of that, but I'm not sure the general solution to second order differential equations applies here. Both functions are dependent on "t".