Find the equation knowing its asymptote in the infinite

[LCSphysicist]

Homework Statement

All below

Relevant Equations

All below

Find all linear differential equations of first order that satisfy this property:

All solutions are asymptotic to the straight line y = 3 - x, when x -> infinity

First i began writing the general equation:

y' + g(x)*y = h(x)

I would say that when x-> infinity, our equations will tends to 3-x (will behave like) and the angular coefficient will tends to -1

so:

-1 + (3-x)*g(x) = h(x)
x-> infinity

But i am not sure if this is right

 

[pasmith]

Start from the most general $y$ which satisfies your condition, and work backwards.

For example, take $y(x) = 3 - x + u(x)$ and work out $y' + g(x)y$.