
Differential Equations Ordinary and Partial Differential Equations Math Forum 
 LinkBack  Thread Tools  Display Modes 
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)/(x4*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  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
FirstOrder, Exact and Linear Differential Equations  summsies  Differential Equations  2  July 24th, 2013 05:24 PM 
2 exact differential equation  helloprajna  Differential Equations  12  July 19th, 2013 09:21 PM 
NonExact Differential equation  Survivornic  Differential Equations  2  September 30th, 2012 02:40 PM 
Exact form, differential equations  jakeward123  Differential Equations  23  March 10th, 2011 02:17 PM 
perimeter of an ellipse  exact equation  realritybugll  Algebra  1  June 9th, 2009 07:15 AM 