My Math Forum Is this allowed?? (First order ODE) Exact Diff Eqn

 Calculus Calculus Math Forum

 October 2nd, 2013, 12:15 PM #1 Newbie   Joined: Oct 2013 Posts: 3 Thanks: 0 Is this allowed?? (First order ODE) Exact Diff Eqn (ycosx + 2xe^y) + (sinx + x^2e^y - 1)y' = 0 (ycosx + 2xe^y) + (sinx + x^2e^y - 1) dy/dx = 0 multiply both sides by dx (ycosx + 2xe^y)dx + (sinx + x^2e^y - 1)dy = 0 integral (ycosx + 2xe^y)dx + integral(sinx + x^2e^y - 1)dy = 0 ysinx + x^2 * e^y + ysinx +x^2 * e^y - y = c 2ysinx + 2x^2 * e^y - y = c
October 2nd, 2013, 05:01 PM   #2
Math Team

Joined: Sep 2007

Posts: 2,409
Thanks: 6

Re: Is this allowed?? (First order ODE) Exact Diff Eqn

Quote:
 Originally Posted by hanilk2006 (ycosx + 2xe^y) + (sinx + x^2e^y - 1)y' = 0 (ycosx + 2xe^y) + (sinx + x^2e^y - 1) dy/dx = 0 multiply both sides by dx (ycosx + 2xe^y)dx + (sinx + x^2e^y - 1)dy = 0
to this point everything is valid.

Quote:
 integral (ycosx + 2xe^y)dx + integral(sinx + x^2e^y - 1)dy = 0
This is not. You cannot integrate y cos(x) 2xe^y with respect to x while treating y as a constant. It isn't constant. Similarly, you cannot integrate sinx+ x^2e^y- 1 with respect to y, treating x as if it were constant.

Quote:
 ysinx + x^2 * e^y + ysinx +x^2 * e^y - y = c 2ysinx + 2x^2 * e^y - y = c

 Tags allowed, diff, eqn, exact, ode, order

,
,

,

,

,

,

,

,

,

,

,

,

,

,

# (y-sin^(2)x)dx sinxdy=0

Click on a term to search for related topics.
 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post arogyth Applied Math 0 July 22nd, 2013 01:22 PM mathkid Calculus 5 September 10th, 2012 03:10 PM lu5t Applied Math 0 April 30th, 2012 09:59 AM foy1der Calculus 2 February 2nd, 2010 07:27 PM hanilk2006 Abstract Algebra 0 December 31st, 1969 04:00 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top