Simple differential equation problem

  • Thread starter NihalRi
  • Start date
  • #1
134
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Homework Statement


Find constants a and b such that y=ax + b is a solution to the differential equation
dy/dx = 4x - 2y

Homework Equations




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
 

Answers and Replies

  • #2
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a = (4-2a) x - 2b (what happened here?)
##
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.
 
  • #3
134
12
##
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.

Thank you
 

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