设z=z(x,y)由x-yz+yez-x-y=0确定,求

admin2021-10-18  21

问题 设z=z(x,y)由x-yz+yez-x-y=0确定,求

选项

答案方程x-yz+yez-x-y=0两边对x求偏导得1-ydz/dx+yez-x-y(dz/dx-1)=0,解得dz/dx=(yez-x-y-1)/y(ez-x-y-1),方程x-yz+yez-x-y=0两边对y求偏导得-ydz/dx-z+ez-x-y+yez-x-y(dz/dx-1)=0,解得dz/dx=[(y-1)ez-x-y+z]/y(ez-x-y-1),则dz=(yez-x-y-1)/y(ez-x-y-1)dx+[(y-1)ez-x-y+z]/y(ez-x-y-1)dy.

解析
转载请注明原文地址:https://kaotiyun.com/show/G8y4777K
0

最新回复(0)