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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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