
#1
Apr1408, 10:20 AM

P: 5

HI there!! i was wondering if you could help me with this..
how do you integrate 2xy/(1+x^2)? Thank you. 



#2
Apr1408, 10:23 AM

Emeritus
Sci Advisor
PF Gold
P: 9,789

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/ 



#3
Apr1408, 10:28 AM

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. 



#4
Apr1408, 11:09 AM

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). 



#5
Apr1408, 12:27 PM

Emeritus
Sci Advisor
PF Gold
P: 9,789

[tex]\frac{dy}{dx} = \frac{2xy}{1+x^2}[/tex] Which is a first order ODE. What methods do you know for solving first order ODE's? 



#6
Apr1408, 08:22 PM

P: 5

by using variable separable method?




#7
Apr1408, 08:41 PM

P: 5

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




#8
Apr1508, 05:16 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,879

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



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