设函数f(x)可导,满足(xex+f(x))ydx+f(x)dy=du(x,y),且f(0)=0,求f(x)及u(x,y))_数学解答

设函数f(x)可导,满足(xex+f(x))ydx+f(x)dy=du(x,y),且f(0)=0,求f(x)及u(x,y))

人气：307 ℃　时间：2020-05-26 11:44:36

解答

ə【(xex+f(x))y】/əy=əf(x)/əxxex+f(x)=f'(x)f'-f-xe^x=0 .①f'=ff=c(x)e^x =>①c'e^x=xe^x,c'=xc(x)=x²/2+Cf(x)= (x²/2+C)e^x.f(0)=0 ,C=0 =>f(x)= (x²/2)e^x..②u(x,y)=∫【0,...