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- #1

- Apr 14, 2013

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I have the following Bernoulli equation:

[tex] 2xyy'+(1+x)y^2=e^{x} [/tex], [tex] x>0 [/tex]

[tex]lim_{x -> 0^{+}} y(x) <\infty [/tex]

The transformation is [tex] u=y^{2} [/tex].

So, [tex] u'+(\frac{1}{x}+1)u=\frac{e^{2x}}{x}[/tex].

How can I find the initial value [tex]u(1)[/tex] so that [tex]lim_{x -> 0^{+}} u(x) <\infty [/tex] ??