such that

The integrating factor is , so:

The point gives:

For the equation is separable.

Problem: The solution in the book gives for and I don't see how to find C_4 because the point isn't on the interval

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- Jan 23rd 2011, 11:44 AMadkinsjrA Linear Equation; IVP; Piecewise Defined Funciton
such that

The integrating factor is , so:

The point gives:

For the equation is separable.

Problem: The solution in the book gives for and I don't see how to find C_4 because the point isn't on the interval - Jan 23rd 2011, 04:31 PMProve It
Your solution looks fine, I don't see how they could have done that either.

On a side note, you could also have used the Integrating Factor method with (and it would probably have been easier, since you already had it). - Jan 24th 2011, 12:47 PMadkinsjr
Yeah, the family of functions is a solution for any value of C, and basically they have which is a constant. The problem is that you can't get to this value...

It turns out that this constant makes the piecewise defined solution continous at x=1 if you change the original intervals to and . The you can say:

However, this isn't correct because on the original interval. But I'm pretty sure I see their mistake now.