∵x²dy+(y-2xy)dx=0 ==>x²dy/dx+(1-2x)y=0
==>dy/y+(1/x²-2/x)dx=0
==>ln|y|-1/x-2ln|x|=ln|C|(C是積分常數(shù))
==>ln|y|=ln|Cx²|+1/x
==>y=Cx²e^(1/x)
∴設(shè)原方程的通解為y=C(x)x²e^(1/x)(C(x)是關(guān)于x的函數(shù))
代入原方程整理得C'(x)=e^(-1/x)/x²
==>C(x)=∫e^(-1/x)d(-1/x)
==>C(x)=e^(-1/x)+C(C是積分常數(shù))
∴y=[e^(-1/x)+C]x²e^(1/x)=x²+Cx²e^(1/x)
故原方程的通解是y=x²+Cx²e^(1/x)(C是積分常數(shù))