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January 25th, 2010, 09:01 PM   #1
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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?
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January 26th, 2010, 08:49 AM   #2
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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?
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January 26th, 2010, 09:45 AM   #3
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Re: Simple differential equation with initial value problem

Yes, that's the only solution.
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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/y]*dy/dt)dt =?(-2*t)dt.
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