# Math Help - Differential equation problem(?)

1. ## Differential equation problem(?)

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 =)

2. 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.

3. 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 ?

4. 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.

5. 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