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henrybrice

Member

Registered: 2009-11-09

Posts: 6

differential equations

I have a differential equation xy'-y=0 (or, if you prefer: x(dx/dy)-y=0) and am meant to decide if there is a common point in this family of functions, i.e. is there a point which they all pass through.

How do I go about checking something like this?

(sorry if my terminology is wrong, I am not studying in English!)

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: differential equations

xy'-y=0 (or, if you prefer: x(dx/dy)-y=0)

Doesn’t

actually mean

?

The way I do it is to solve the differential equation (by separating the variables and integrating) getting the general solution

. Hence the solution family is the set of all nonvertical straight lines through the origin, so

is the common point you are looking for.

henrybrice

Member

Registered: 2009-11-09

Posts: 6

Re: differential equations

y' is indeed meant to be dy/dx, sorry, my typo!

wouldn't the solution be y=x+c? And in that case wouldn't each one cross the y axis at a different place depending on c?

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: differential equations

wouldn't the solution be y=x+c? And in that case wouldn't each one cross the y axis at a different place depending on c?

No, after integration you wind up with

Putting both of these over e will turn the addition on the RHS to multiplication.

---

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

henrybrice

Member

Registered: 2009-11-09

Posts: 6

Re: differential equations

Okay! Thanks very much for all the help