Given the differential equation f' =2x-y, is there a linear solution (that is, a line of the form y=mx+b)?

Answer 1

You say f’(x)=2x-y this implies y doesn’t equal f(x)

i assume you mean y’=2x-y which is in the form y’+Py=Q

I(x)=e^(integral P dx)

This is a first order linear nonhomogeneous differential equation. It has a few approaches but one specific formula works perfectly.

y=1/I(x)[integral Q(x)I(x) dx + C]

when you solve that, you will have your answer