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Math Help - Differential equation problem(?)

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    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 =)
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    Quote Originally Posted by AshleyT View Post
    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.
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    Quote Originally Posted by mr fantastic View Post
    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 ?
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    Quote Originally Posted by AshleyT View Post
    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.
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    Quote Originally Posted by mr fantastic View Post
    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
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