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- TL;DR Summary
- I have been thinking about the differential equation for the motion of a free falling object without air resistance (on my own, not as homework), which is in the form ##y^2y''+K=0## with ##K## as a positive constant. I'm looking for advice on a first step to solve this equation.

That's pretty much it. If there is a very basic strategy that I am forgetting from ODEs, please let me know, though I don't recall any strategies for nonlinear second order equations.

I've tried looking up "motion of a free falling object" with various specifications to try to get the solution to this equation, but the sources I find still always assume ##g## does not vary with distance. I have also tried looking up "motion of a charge in a coulomb field" but to no avail.

Thank you in advance!

I've tried looking up "motion of a free falling object" with various specifications to try to get the solution to this equation, but the sources I find still always assume ##g## does not vary with distance. I have also tried looking up "motion of a charge in a coulomb field" but to no avail.

Thank you in advance!