∵(1+x^2)ydx-(2-y)xdy=0
==>(1+x^2)ydx=(2-y)xdy
==>(2-y)dy/y=(1+x^2)dx/x
==>(2/y-1)dy=(1/x+x)dx
==>2ln│y│-y=ln│x│+x^2/2+ln│C│ (C是常数)
==>y^2*e^(-y)=Cxe^(x^2/2)
==>y^2=Cxe^(y+x^2/2)
∴原方程的通解是y^2=Cxe^(y+x^2/2).