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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
  2. jcsd
  3. Apr 2, 2016 #2


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    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
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