# Integration Problem

by lost_2
Tags: integration
 P: 5 HI there!! i was wondering if you could help me with this.. how do you integrate -2xy/(1+x^2)? Thank you.
Emeritus
PF Gold
P: 9,789
 Quote by lost_2 HI there!! i was wondering if you could help me with this.. how do you integrate -2xy/(1+x^2)? Thank you.
Welcome to the forums,

Your question is incomplete. What are you integrating with respect to? Is y a function of x or vice versa?

As an aside, feel free to post a new topic for each new question, you don't need to tag your question on the end of others/
 P: 5 Hey! Thanks for the quick reply.. Coz it a similar qns so i posted together with this. That equation is the gradient of a curve. So it's just to integrate with respect to x? How do you go about doing it? Thank you.
P: 5

## Integration Problem

Anyways this is the whole qns.

find the equation of the curve in the xy plane that passes through (1,2) and whose tangent line at a point (x,y) has a slope of -2xy/(1+x^2).
Emeritus
PF Gold
P: 9,789
 Quote by lost_2 Anyways this is the whole qns. find the equation of the curve in the xy plane that passes through (1,2) and whose tangent line at a point (x,y) has a slope of -2xy/(1+x^2).
Thanks, it's always a good idea to post the entire question. So you know that,

$$\frac{dy}{dx} = -\frac{2xy}{1+x^2}$$

Which is a first order ODE. What methods do you know for solving first order ODE's?
 P: 5 by using variable separable method?
 P: 5 is the answer y(1+x^2)= c?
 Math Emeritus Sci Advisor Thanks PF Gold P: 38,900 You have not yet used the fact that the curve passes through (1, 2).

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