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Math 1 - y 1‘ J 111m 211 M C ly|g.elnx2 c ‘...

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Unformatted text preview: y 1‘ J: ' . 111m: 211': M+ C ly|g.elnx2+c ‘ i343).- %d:ecx2 :%fi§,-W):. 9x2. 8. Separate the variables and integrate. d_y_ x dx“y x—l l —dy=(1+ 1 )dx y x—l 1n|y| =x+lnlx— 1|+C Iyl =ex+ln|x-II+C y(x)= :IzeCe‘e'“ 'x ll Letting D = iec ,y(x) 2 De" Ix — 1|. It is impor- tant to note that this solution is not differentiable at x = 1 and further information (perhaps in the form of an initial condition) is needed to remove the ab- solute value and determine the interval of existence. l4. 1 E111(1 + y?) = —t2 + C 1 + y2 = e—2fl+c = gee—2:2 1+y2 =Ae‘2'2 ...
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