Question

I need to solve this second order differential equation, (GM)/(R-x^2)=d^2x/d^2t
Where G,M and R are constants, x being the dependant and t being the independant

Answer 1

Just including a better looking version of th equation\[(GM)/(R-x^2)=d^2x/d^2t\]

Also, would very much appreciate it if an explanation was provided, thanks

Answer 2

Perhaps it's a variable-separable equation.
If that's the case, then you can transpose (sorry for the term) d^2t to the left side and (R-x^2) to the right side, and then integrate both sides.

Answer 3

I think that process is only for first order differntial equations

Answer 4

But I guess you can just integrate it twice. :)
By the way, is that\[d^2t\]or\[dt^2\]?

Answer 5

dt^2 sorry, i tried that method earlier, but it turns out the method does not extend to second order differntial equations

Answer 6

uh anyon

Answer 7

Are you sure you've written this equation down correctly? It look likes you're trying to model a body falling in a (Newtonian) gravitational field. But if that is right, your equation isn't quite right.