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 Differential Equations Ordinary and Partial Differential Equations Math Forum

 September 30th, 2012, 10:40 AM #1 Newbie   Joined: Sep 2012 Posts: 14 Thanks: 0 Exact differential equation Hey guys, I've been trying to solve a differential equation, I checked 20 times but it's not the right answer.. It's dy/dx=(3*x^3+y)/(-x-4*y^3) wich equals (3*x^3+y)dx+(x+4*y^3)dy=0 So My=1 and Nx=1, so the equation is exact Then I do the integer of 3*x^3+y, which gives 3/4*x^4+x*y+(a function of y) I do all the steps and I find the function of y, which is y^4 so my answer is 3/4*x^4+x*y+y^4 but it says it's not the right answer. Could anyone help me please? September 30th, 2012, 10:57 AM #2 Senior Member   Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Exact differential equation You have correctly expressed the ODE in differential form: You have correctly determined the equation is exact. So, we set: Now differentiate with respect to y: Hence, the solution is given implicitly by: It appears the only thing you have left out is the constant. September 30th, 2012, 11:14 AM #3 Newbie   Joined: Sep 2012 Posts: 14 Thanks: 0 Re: Exact differential equation That's what I thought but I keep entering this answer and it says that it's wrong... maybe there's a problem on the site.. Thanks a lot! October 1st, 2012, 07:02 PM #4 Math Team   Joined: Sep 2007 Posts: 2,409 Thanks: 6 Re: Exact differential equation The way I would have done this problem is this: to say that is an exact equation means that there exist a function F(x,y) such that . So we must have and differentiating with respect to x treats y as a constant, integrating, treating y as a constant, where, because we are treating y as a constant, the "constant of integration" may be a function of y, g(y). Differentiating that with respect to y, . That is, we must have so that where, because g is a function of y only, C really is a constant. That is . Because the original differential equation was "dF= 0", F is a constant: and we can combine the two constant to get . Tags differential, equation, exact Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post summsies Differential Equations 2 July 24th, 2013 05:24 PM helloprajna Differential Equations 12 July 19th, 2013 09:21 PM Survivornic Differential Equations 2 September 30th, 2012 02:40 PM jakeward123 Differential Equations 23 March 10th, 2011 02:17 PM realritybugll Algebra 1 June 9th, 2009 07:15 AM

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