- Thread starter
- #1
- Apr 14, 2013
- 4,267
Hello!!!
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] ??
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] ??