Matematické Fórum

p4too · 20. 12. 2015 22:09

Ahojte, mam problem s prikladom, opet.

$y'=\frac{y+2}{x+y-1}$
$subs.: y=m-2$
$x=n+3$
$m'=\frac{m}{n+m}$
$m'=\frac{m}{n+m}*\frac{\frac{1}{n}}{\frac{1}{n}}$
$m'=\frac{\frac{m}{n}}{1+\frac{m}{n}}$
$subs: u=\frac{m}{n}$
$m=un$
$m'=u'n+u$
$u'n+u=\frac{u}{1+u}$
$u'n=\frac{-u^2}{1+u}$
$-\frac{1+u}{u^2}du=\frac{dn}{n}$
$-[ln|u|-\frac{1}{u}]=ln(c*n)$
$\frac{1}{u}-ln|u|=ln(c*n)$
$lne^\frac{1}{u}-ln|u|=ln(c*n)$
$ln\frac{e^\frac{1}{u}}{u}=ln(c*n)$
$\frac{e^\frac{1}{u}}{u}=c*n$
$\frac{e^\frac{1}{\frac{m}{n}}}{\frac{m}{n}}=c*n$
$\frac{e^\frac{n}{m}}m=c$
$\frac{e^\frac{x-3}{y+2}}{y+2}=c$
obecne riesenie, problem je ze to malo vyst
$y+2=ce^w$
kde
$w=-2arctg\frac{x/2}{x_0/2}$

kde som spravil chybu