Simple differential equation problem

[NihalRi]

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

 

[BvU]

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.

 

[NihalRi]

$a=4x-2 (ax+b) \Leftrightarrow a=4x-2ax-2 b \Leftrightarrow a= (4-2a) x-2 b$ 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