几道微积分题

显示全部楼层 · 2011-12-24 00:41:19

解：1.∵xy'=yln(y/x) ==>y'=(y/x)ln(y/x)
==>xt'+t=tlnt(令y=xt)
==>dt/[t(lnt-1)]=dx/x
==>d(lnt-1)/(lnt-1)=dx/x
==>ln│lnt-1│=ln│x│+ln│C│(C是积分常数)
==>lnt-1=Cx
...

千问 · 2011-12-24 00:41:19

解：1.∵xy'=yln(y/x) ==>y'=(y/x)ln(y/x)
==>xt'+t=tlnt(令y=xt)
==>dt/[t(lnt-1)]=dx/x
==>d(lnt-1)/(ln...

千问 · 2011-12-24 00:41:19

1.xy'=y ln（y/x） y=xu, y'=xu'+uxu'+u=ulnudu/(ulnu-u)=dx/xln|x|+C0=ln|(lnu-1)|C1|x|=|lnu-1|通解C1|x|=|ln(|y/x|-1)|2.xy'-y=x tan（y/x）xdy-ydx=xtan(y/x)dx(xdy-ydx)/x...