中文摘要：

目的对函数方程f（xy）=xf（y）＋yf（x），（x，y）∈R^2进一步研究。方法用数学分析的方法，借助微分方程的可解性展开研究。结果该方程在，没有可微的条件下，给出了它的一般解和所有连续解，并且将其推广到两种一般情形。结论推广了数学分析中的经典命题，从而使它的应用更加广泛。

英文摘要：

Aim The purpose is to make a further study on functional equationf（xy） =xf（y） ＋if（x）, （x,y） ∈ R^2. Methods The method is to use the mathematical analysis with the help of the solvability of the differential equation. Results The result is that this equation in which f can not be differentiated,has given its general and all continous solutions and further more, the solutions are extended to two general situations. Conclusion The classical proposition of the mathematical analysis thus is extended to wider application.