math 310 a2 Sol

# math 310 a2 Sol - MATH 310-3 Differential Equations...

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MATH 310-3 Fall 2011 Diﬀerential Equations Homework Set 2 Some Solutions The following solutions are not necessarily complete, but should highlight the main points for most questions. If you have any further questions regarding the problems and solutions, feel free to discuss them on WebCT. Solutions marked by * are taken from the publisher’s Instructor’s Solutions Manual for the textbook by Boyce and DiPrima, 9th edition (Wiley), while solutions marked by (which appear to have been typed with a typewriter. . . ) are from the publisher’s Student Solutions Manual; in some cases I have added comments in [brackets]. Section 1.1: * Section 1.1 # 10 : * Section 1.1 # 26 : [If sketching the direction ﬁeld by hand, one can begin by using the isoclines , curves on which y 0 is constant. In this case, we have y 0 = - 2 + t - y , so y 0 = c when - 2 + t - y = c , or y = t - (2 + c ); that is, all points on each straight line of slope dy/dt = 1 have the same value of y 0 in the direction ﬁeld. Hence we have, for instance,

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math 310 a2 Sol - MATH 310-3 Differential Equations...

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