令y^2＝u,则方程变为du/dx+2xu=xe^(－x^2).
齐次方程的通解为u＝Ce^(－x^2).
特解设为u＝e^(－x^2)*g(x),则
易知g(x)满足g'(x)=x,可取g(x)=x^2/2.
于是通解为u＝(x^2/2+C)e^(－x^2).回代u＝y^2即可.