Find the equation knowing its asymptote in the infinite

  • #1
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32

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
 

Answers and Replies

  • #2
pasmith
Homework Helper
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485
Start from the most general [itex]y[/itex] which satisfies your condition, and work backwards.

For example, take [itex]y(x) = 3 - x + u(x)[/itex] and work out [itex]y' + g(x)y[/itex].
 
Last edited:

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