设函数f(x,y)可微,=ecoty,求f(x,y).

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问题 设函数f(x,y)可微,=ecoty,求f(x,y).

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答案[*] 由[*] 得C=0,即f(0,y)=siny. 又由[*]=一f(x,y),得lnf(x,y)=一x+lnφ(y). 即f(x,y)=φ(y)e一x,由f(0,y)=siny,得φ(y)=siny,所以f(x,y)=e一xsiny.

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