1. Not finding help here? Sign up for a free 30min 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!

Simple differential equation problem

  1. Apr 2, 2016 #1
    1. The problem statement, all variables and given/known data
    Find constants a and b such that y=ax + b is a solution to the differential equation
    dy/dx = 4x - 2y

    2. Relevant equations


    3. The attempt at a solution
    I already have the solution that is:
    a=4x-2 (ax+b) (I'm fine with this part)
    a = (4-2a) x - 2b (what happened here?)

    4-2a=0 (why?) a= -2b (why?)
    a= 2
    b=-1
     
  2. jcsd
  3. Apr 2, 2016 #2

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    ##
    a=4x-2 (ax+b) \Leftrightarrow a=4x-2ax-2 b \Leftrightarrow a= (4-2a) x-2 b ## can only be true for all x if ##(4-2a)=0##. What remains is ## a = -2b ## . Pick an a and a b follows.
     
  4. Apr 2, 2016 #3
    Thank you
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted