1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Integrating factor to solve this?

  1. Mar 15, 2017 #1
    1. The problem statement, all variables and given/known data
    ##cos t \frac{dv}{dt} + (sin t) t = \frac{GM}{b^2 }\sin^3 t ##

    2. Relevant equations


    3. The attempt at a solution

    im pretty stuck to be honest. It almost looks like a product rule on the LHS but it has the wrong sign, RHS I've tried writing ##sin^3 t## as ##(1-cos^2t)\sin t## etc, pretty unsure what integration factor I need.

    Thanks in advcance.
  2. jcsd
  3. Mar 15, 2017 #2
    Hi binaqsss:

    I suggest trying the substitution x = sin(t).

  4. Mar 15, 2017 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    If you wrote the problem correctly, then you just have
    $$\frac{dv}{dt} = - t \tan t + a \frac{ \sin^3 t }{\cos t} = - t \tan t + a \sin^2 t \, \tan t,$$
    so ##v = - \int t \tan t \, dt + a \int sin^2 t \, \tan t \, dt##. The integration in the first term involves some non-elementary functions.
  5. Mar 15, 2017 #4


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Did you perhaps mistype it and mean instead:$$
    \cos t \frac{dv}{dt} + (\sin t) \color{red}{v} = \frac{GM}{b^2 }\sin^3t \text{ ?}$$
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted