求dy/dx=(x-y+5)/(x+y-2)

题目

求dy/dx=(x-y+5)/(x+y-2)

答案

dy/dx=(x-y+5)/(x+y-2)=[(x+3/2)-(y-7/2)]/[(x+3/2)+(y-7/2)]令 v=y-7/2,u=x+3/2,原方程化为 dv/du=(u-v)/(u+v) 变为齐次方程.再令 p=v/u,方程化为 p+udp/du=(1-p)/(1+p),则化成可分离变量型 (1+p)dp/(1-2p-p^2)=du/...