# Differential equation problem(?)

• Apr 7th 2009, 02:37 AM
AshleyT
Differential equation problem(?)
Quote:

A curve passing through the point(1, 1) has the property that, at each point P of the curve the gradient of the curve is 1 less than the gradient of OP. Find the equation of the curve
Have no idea how to do this so any help would be greatly appreciated :), a poke in the right direction?
Thanks =)
• Apr 7th 2009, 02:42 AM
mr fantastic
Quote:

Originally Posted by AshleyT
Have no idea how to do this so any help would be greatly appreciated :), a poke in the right direction?
Thanks =)

Solve $\frac{dy}{dx} = \frac{y}{x} - 1$ subject to the condition that y = 1 when x = 1.
• Apr 7th 2009, 03:39 AM
AshleyT
Quote:

Originally Posted by mr fantastic
Solve $\frac{dy}{dx} = \frac{y}{x} - 1$ subject to the condition that y = 1 when x = 1.

Thankyou very much for your reply :).
Where does y / x come from though if i may ask :)?
• Apr 7th 2009, 06:19 AM
mr fantastic
Quote:

Originally Posted by AshleyT
Thankyou very much for your reply :).
Where does y / x come from though if i may ask :)?

Another poke ....?

I assume that O is the origin and that P has coordinates (x, y). Then y/x is the gradient of the line segment OP.
• Apr 8th 2009, 04:13 AM
AshleyT
Quote:

Originally Posted by mr fantastic
Another poke ....?

I assume that O is the origin and that P has coordinates (x, y). Then y/x is the gradient of the line segment OP.

Thank-you :)