两未知函数的一阶线性偏微分方程组的一般解

GENERAL SOLUTRONS OF LINEAR PARTIAL DIFFERENTIAL EQUATIONS OF ORDER 1 FOR TWO UNKNOW FUNCTIONS

证明了，若ａｉ，ｂｉ（ｉ＝０，１，２）皆为ｘ１、ｘ２的三次连续可微函数，ａ２ｂ１－ａ１ｂ２≠０，Ａ＝ａ０＋ａ１Ｄ１＋ａ２Ｄ２，Ｂ＝ｂ０＋ｂ１Ｄ１＋ｂ２Ｄ２，Ｄｉ＝ｘｉ，ｉ＝１，２，则必存在线性偏微分算子Ｃ、Ｄ，满足ＡＣ＝ＢＤ，并给出了Ｃ、Ｄ的计算公式。

This paper proves, if a i,b i (i=0,1,2) are functions of x 1、x 2, whose differentials of order 3 are continuous, a 2b 1-a 1b 2≠0,A=a 0+a 1D 1+a 2D 2,B=b 0+b 1D 1+b 2D 2,D i=   x i, i=1,2, then there must exist linear partial diffrential operotors C、D, satisfging AC=BD, and the calculation formulas of C、D are given.