设f(u,v)具有二阶连续偏导数,且满足

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问题 设f(u,v)具有二阶连续偏导数,且满足

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答案[*]=fy’1+xf’2, [*]=y(yf’’11+xf’’12)+f’2+x(yf’’21+xf’’22)=y2f’’11+2xyf’’+x2f’’22+f’2, [*]=xf’1-yf’2, [*]=x(xf’’11-yf’’12)-f’2-y(xf’’21-yf’’22)=x2f’’11-2xyf’’12+y2f’’22-f’2, [*]=(x2+y2)(f’’11+f’’22)=x2+y2

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