2复变画数与和换 1901 Complex Analysis and Integral Transform 又n=v,l=-v,联立得u=6xy,l=3x2-3y2 故=3x2y+0)=3x2+01(y)=3x2-3y得 (y)=-3y2,(y)=-y3+C故u=3x2y-y3+C 同理可得ν=3xy2-x3+C 由已知等式可知:C1=C,=C复变函数与积分变换 Complex Analysis and Integral Transform 2 2 又u v u v u xy u x y       x y y x x y = = − = = − , , 6 , 3 3 联立得 2 2 2 2 3 ( ) 3 ( ) 3 3 y 故 u x y y u x y x y = + = + = −   由   得 ' 2 3 2 3 ( ) 3 , ( ) 3   y y y y C u x y y C = − = − + = − + 故 v = xy − x +C 2 3 同理可得 3 由已知等式可知：C1 = C2 = C