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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:
 

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differential, equation, initial, problem, simple 
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