y(x) = ln(C1*x^2/2+_C2)
令p=y'==》原方程化为xp'+xp^2-p=0 <1>-->p'=p/x-p^2
代换,令p=ux-->p'=u'x+u=u-p^2=u-x^2*u^2==>u'x=-u^2*x^2-->u'=-u^2*x
-->du/u^2=-xdx-->1/u=x^2/2+C1-->p=y'= 2*x/(x^2+2*C1)-->...
y= ln(C1*x^2/2+C2)
dy/dx =e^(x+y)
∫e^(-y)dy = ∫e^x dx
-e^(-y) = e^x + C
记得采纳哦
我是XXO