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- Jan 29th 2011, 02:03 PM #1

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## help with a problem

Hey guys, i just started a new course in differential equations and im kinda having a hard time. Heres one of the problems I am having difficulty with:

Verify that the piecewise-defined function

is a solution of the differential equations on

Thanks!

- Jan 29th 2011, 02:07 PM #2

- Jan 29th 2011, 02:12 PM #3

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- Jan 29th 2011, 02:13 PM #4

- Jan 29th 2011, 02:27 PM #5

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- Jan 29th 2011, 03:33 PM #6

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Not quite. You cannot just choose two values of x. If x is any positive number, then so that y'= 2x. The equation xy'-2y = 0 becomes so the equation is satisfied for any positive x. If x is negative, . Do the same with that. Most importantly, what happens at x= 0? In particular what is the derivative of y at x= 0? (You can't just differentiate and set x= 0 because the derivative involves a limit from both sides: If x= 0 and h is positive, then x+h= 0+ h= h is positive, if h is negative, x+ h= h is negative.

If those two limits are the same, that is the dervative at x= 0. If they are not, the function is not differentiable at x= 0.