Solving an ODE: Seeking Help on Mechanics Problem

[Pyroadept]

Homework Statement

A point in a mechanics problem where I have to solve the ODE (dS/dx)^2 + mw^2x^2 = a

where m,w^2 are constants

Homework Equations

The Attempt at a Solution

Hi everyone,
We haven't actually covered how to solve these in my ODEs class yet (obviously my mechanics lecturer doesn't know this!). Please could someone point me in the right direction as to how to start it?
Thanks for any help!

 

[Mark44]

Write the equation as (dS/dx)² = a - mw²x, and then take the square root of both sides. Don't forget to include +/- on the right side.

Now you have two separable differential equations (one for +, one for -).