1. y(xy+1)dx+x(1+xy+x^2y^2)dy=0
=>xy^2dx+ydx+xdy+x^2ydy+x^3y^2dy=0
=> ydx+xdy+x^2ydy+ xy^2dx+ x^3y^2dy=0
^^^^^^^ ^^^^^^^^^^^^^^
=> d(xy)+ xyd(xy) + x^3y^2dy=0
同除x^3y^3=>(xy)^-3d(xy) +(xy)^-2d(xy) + y^-1dy=0
積分=>-1/xy-1/2(xy)^2+lny=c
2. ydx+(x+x^3y^2)dy=0, y(e^-2/2)=e^2
ydx + xdy+x^3y^2dy=0
=>d(xy) + x^3y^2dy=0
同除x^3y^3=>(xy)^-3d(xy) +y^-1dy=0
積分=>-1/2(xy)^2+lny=c
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 114.32.124.166