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Unformatted text preview: t 2 x 3 + 3 t4 x, we have f ( t,x ) t = 2 tx 3 +3 , here 4 x is a constant with respect to t , so the derivative is 0, and x 3 is also a constant, so t 2 x 3 when taking derivative against t we have 2 tx 3 . Therefore nding partial derivative is as easy as to nd ordinary derivative.This theorem only guarantees a solution dened for t in an open interval, which might be a bounded interval. For example x = x 2 , we see that x ( t ) =1 t + c is the general solution, if c =2 then the solution is only dened on interval (0, 2) as x ( t ) =1 t2 will become undened at t = 2 .Some time we could have more than one solution that satises the same initial condition, for example, for x = x 2 3 and x (0) = we have two dierent solution, one is x ( t ) = 0 another one...
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This note was uploaded on 10/04/2011 for the course MAP 4231 taught by Professor Dr.han during the Spring '11 term at UNF.
 Spring '11
 Dr.Han

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