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February 7th, 2008, 09:54 AM  #1 
Newbie Joined: Feb 2008 Posts: 2 Thanks: 0  an ordinary differential equation
I cannot solve this for the life of me. 3(1+(x^2))(dy/dx) = 2xy((y^3)1) AT LEAST give me a way to rearrange it to be able to solve it with integrals. thanksss 
February 7th, 2008, 09:59 AM  #2 
Senior Member Joined: May 2007 Posts: 402 Thanks: 0 
2x/(1+x^2)dx=3*dy/(y(y^3)1)

February 7th, 2008, 11:22 AM  #3  
Newbie Joined: Feb 2008 Posts: 2 Thanks: 0  Quote:
 
February 8th, 2008, 08:19 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 21,035 Thanks: 2272 
3(1+(x²))(dy/dx) = 2xy((y^3)1) For y ≠ 0, dividing by (1 + x²)²y^4 and rearranging gives ((1 + x²)(3y^4)dy/dx  (1  y^3)(2x))/(1 + x²)² = 0. Integrating that gives (1  y^3)/(1 + x²) = C, where C is a constant. Hence y = 1/³√(1  C(1 + x²)) (where C is negative or greater than 1, so that y is defined for all values of x) or y ≡ 0. 

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