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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
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Quote:
 Originally Posted by BlackOps int([1/y]*dy/dt) = int(-2*t)
That should have been ?([1/y²]*dy/dt)dt =?(-2*t)dt.

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