（常數(shù)變易法）
∵y'+2xy=0 ==>dy/y=-2xdx
==>ln│y│=-2x²+ln│C│ (C是積分常數(shù))
==>y=Ce^(-x²)
∴設(shè)微分方程y'+2xy+2(x^3)=0的通解為y=C(x)e^(-x²)(C(x)表示關(guān)于x的函數(shù))
∵y'=C'(x)e^(-x²)-2xC(x)e^(-x²)
代入原方程得C'(x)e^(-x²)+2x³=0
==>C'(x)=-2x³e^(x²)
==>C(x)=-2∫x³e^(x²)dx
=-∫x²e^(x²)d(x²)
=-x²e^(x²)+∫e^(x²)d(x²) (應(yīng)用分部積分法)
=-x²e^(x²)+e^(x²)+C （C是積分常數(shù)）
=(1-x²)e^(x²)+C
∴y=C(x)e^(-x²)=[(1-x²)e^(x²)+C]e^(-x²)=1-x²+Ce^(-x²)
故微分方程y'+2xy+2(x^3)=0的通解是y=1-x²+Ce^(-x²)（C是積分常數(shù)）.