 My Math Forum Simple differential equation with initial value problem

 Differential Equations Ordinary and Partial Differential Equations Math Forum

 January 25th, 2010, 09:01 PM #1 Newbie   Joined: May 2008 Posts: 29 Thanks: 0 Simple differential equation with initial value problem Hello, here is the problem: dy/dt = -2*t*y^2, y(1) = 0 Now, according to the rules, I should first find the general solution by separation of variables: int([1/y]*dy/dt) = int(-2*t) after integrating both parts, I get: y = 1/([t^2] + 2c) so the general solution is: y = 1/([t^2] + 2c), AND 0 for ALL t. (because during separation of variables i was dividing by y^2, excluding the fact that y may be zero) am I right up until now? (for me seems yes..because I solved the same problem with another initial value) but now, for the initial value of y(1) = 0 I'm getting stuck.. because if I will plug t = 1, and y = 0 in y = 1/([t^2] + 2c), it will not make sense... am I missing something? January 26th, 2010, 08:49 AM #2 Newbie   Joined: May 2008 Posts: 29 Thanks: 0 Re: Simple differential equation with initial value problem ok my guess now that the solution to this initial value problem is: y(t) = 0, cuz only this makes sense... what do u think? January 26th, 2010, 09:45 AM #3 Senior Member   Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3 Re: Simple differential equation with initial value problem Yes, that's the only solution. January 27th, 2010, 03:29 AM   #4
Global Moderator

Joined: Dec 2006

Posts: 21,111
Thanks: 2326

Quote:
 Originally Posted by BlackOps int([1/y]*dy/dt) = int(-2*t)
That should have been ?([1/y]*dy/dt)dt =?(-2*t)dt. Tags differential, equation, initial, problem, simple 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 Thelair Differential Equations 1 November 19th, 2013 08:24 AM philip Differential Equations 0 February 16th, 2013 11:59 AM newslang Differential Equations 3 February 21st, 2012 12:52 PM aaron-math Differential Equations 4 October 31st, 2011 02:40 AM BlackOps Differential Equations 1 March 1st, 2010 07:41 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top      