设函数f(x,y)具有一阶连续偏导数,且(x,y)=yeydx+x(1+y)eydy,f(0,0)=0,则f(x,y)=_______.

admin2021-01-25  39

问题 设函数f(x,y)具有一阶连续偏导数,且(x,y)=yeydx+x(1+y)eydy,f(0,0)=0,则f(x,y)=_______.

选项

答案xyey

解析 f’k=yey,f’y=x(1+y)ey,f(x,y)=∫yeydx=xyey+c(y),故f’y=xey+xyey+c’(y)=xey+xyey,故c’(y)=0,由f(0,0)=0,即f(x,y)=xyey
转载请注明原文地址:https://kaotiyun.com/show/dVx4777K
0

最新回复(0)