- #1
LazyPhysicist1
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- TL;DR Summary
- I need help solving the nonlinear photon trajectory diffeq near a mass as derived by the Schwarzschild metric.
Using the null geodesic and the Schwarzschild metric, this differential equation for photon trajectory near a mass can be derived, where u is r_s /2r:
View attachment 349924
Though this nonlinear ode is fairly easy to approximate (which I already have), I'm looking for an analytic solution or an approximate analytic solution. No online calculators work, except Wolfram (for which I don't have pro), which gives me an unusably complicated solution; https://www.wolframalpha.com/input?i=y''+=+3y^2-y
Is there a way I can better solve this differential equation/approximate an analytical solution? Thanks.
View attachment 349924
Though this nonlinear ode is fairly easy to approximate (which I already have), I'm looking for an analytic solution or an approximate analytic solution. No online calculators work, except Wolfram (for which I don't have pro), which gives me an unusably complicated solution; https://www.wolframalpha.com/input?i=y''+=+3y^2-y
Is there a way I can better solve this differential equation/approximate an analytical solution? Thanks.