February 6th, 2016, 11:27 PM  #1 
Newbie Joined: Feb 2016 From: israel Posts: 17 Thanks: 3  ODE system
Hi guys, I need some help solving the next ODE system: w'+2*U*sin(psi)=0 wv'+2UV*sin(psi)=V'' WU'+(U^2V^2)*sin(psi)=mTsin(psi)+U'' m,T,psi are constants BCE's: U=V=W=0 @ x=0, U>0 as x>infinity, V>(1) as x>infinity Some guidance would be greatly appreciated. shai Last edited by skipjack; February 7th, 2016 at 02:55 PM. 
February 7th, 2016, 06:21 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
You appear to have three equations in four unknown functions, y, U, V, and W (I am assuming the "w" in the first two equations was intended to be "W"). You aren't going to be able to solve three equations for four unknowns.

February 7th, 2016, 01:31 PM  #3 
Global Moderator Joined: May 2007 Posts: 6,807 Thanks: 717  I see U,V, and W, but no y. It looks like 3 equations in 3 unknowns.

February 7th, 2016, 02:55 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,935 Thanks: 2209 
I would guess that "v" and "w" should have been "V" and "W" respectively. Where did the problem come from? 
February 8th, 2016, 04:16 AM  #5 
Newbie Joined: Feb 2016 From: israel Posts: 17 Thanks: 3 
My mistake, I only have u,v, and w (no y). This problem comes from boundary layer theory (fluid dynamics). The equations describe the flow over a spinning cone (similarity analysis of the NavierStokes equations). I'm going to try and solve it with Maple numerically... Last edited by skipjack; February 8th, 2016 at 05:33 AM. 
February 8th, 2016, 09:11 AM  #6 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
Sorry! There was a bit of dirt on my screen that made a "v" look like a "y".

February 9th, 2016, 06:03 PM  #7 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,834 Thanks: 650 Math Focus: Yet to find out. 
Have you tried solving it using Laplace Transform? I had a bit of a try but am a bit rusty, and it was getting messy pretty quick. Plus, I have no idea whether it would be a suitable method. Also, for the sakes of readability... $\displaystyle W' + 2U\sin(\psi) = 0$ $\displaystyle WV' + 2UV\sin(\psi) = V''$ $\displaystyle WU' + (U^2  V^2) \sin(\psi) = mT\sin(\psi) + U''$ Last edited by skipjack; February 9th, 2016 at 11:34 PM. 

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