Integrating -2xy/(1+x^2): Solution

[lost_2]

HI there! i was wondering if you could help me with this..

how do you integrate -2xy/(1+x^2)?

Thank you.

 

[Hootenanny]

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/

 

[lost_2]

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.

 

[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).

 

[Hootenanny]

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?

 

[lost_2]

by using variable separable method?

 

[lost_2]

is the answer y(1+x^2)= c?

 

[HallsofIvy]

You have not yet used the fact that the curve passes through (1, 2).