设z=f(x,y)二阶可偏导,,且f(x,0)=1,f’y=(x,0)=x,则f(x,y)=________.

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问题 设z=f(x,y)二阶可偏导,,且f(x,0)=1,f’y=(x,0)=x,则f(x,y)=________.

选项

答案y2+xy+1

解析 ,z=y2+xy+C,因为f(x,0)=1,所以C=1,于是z=y2+xy+1.
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