高等数学如下图谢谢
log(x^2+y^2)是什么函数？难倒没有“底”么？是不是自然对数ln(x^2+y^2)呀？？
y^2=cosh(xy)+ln(x^2+y^2)
===> 2yy'=sinh(xy)*(y+xy')+[1/(x^2+y^2)]*(2x+2yy')
===> 2yy'=y*sinh(xy)+xy'*sinh(xy)+[2x/(x^2+y^2)]+[2y/(x^2+y^2)]y'
===> [2y-x*sinh(xy)-2y/(x^2+y^2)]y'=y*sinh(xy)+[2x/(x^2+y^2)]
===> y'=[y*sinh(xy)+2x/(x^2+y^2)]/[2y-x*sinh(...全部
log(x^2+y^2)是什么函数？难倒没有“底”么？是不是自然对数ln(x^2+y^2)呀？？
y^2=cosh(xy)+ln(x^2+y^2)
===> 2yy'=sinh(xy)*(y+xy')+[1/(x^2+y^2)]*(2x+2yy')
===> 2yy'=y*sinh(xy)+xy'*sinh(xy)+[2x/(x^2+y^2)]+[2y/(x^2+y^2)]y'
===> [2y-x*sinh(xy)-2y/(x^2+y^2)]y'=y*sinh(xy)+[2x/(x^2+y^2)]
===> y'=[y*sinh(xy)+2x/(x^2+y^2)]/[2y-x*sinh(xy)-2y/(x^2+y^2)]
即：dy/dx=[y*sinh(xy)+2x/(x^2+y^2)]/[2y-x*sinh(xy)-2y/(x^2+y^2)]
满足y^2=cosh(xy)+ln(x^2+y^2)的一组解为(x,y)=(0,1)。
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