设f(x,y)满足=2,f(x,0)=1,f’y(x,0)=x,则f(x,y)=________.

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问题 设f(x,y)满足=2,f(x,0)=1,f’y(x,0)=x,则f(x,y)=________.

选项

答案y2+xy+1.

解析=2y+φ1(x),因为f’y(x,0)=x,所以φ1(x)=x,即=2y+x,再由=2y+x得f(x,y)=y2+xy+φ2(x),因为f(x,0)=1,所以φ2(x)=1,故f(x,y)=y2+xy+1.
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