y=2x *arctan(y/x)
那么对x 求导得到
y'=2arctan(y/x) +2x *1/(1+y^2/x^2) *(y/x)'
=2arctan(y/x) +2x *1/(1+y^2/x^2) *(xy'-y)/x^2
=2arctan(y/x) +2x *(xy'-y)/(x^2+y^2)
化简得到
(x^2+y^2)y'=2(x^2+y^2)arctan(y/x) +2x *(xy'-y)
即(y^2-x^2)y'=2(x^2+y^2)arctan(y/x) -2xy
所以y'=[2(x^2+y^2)arctan(y/x) -2xy] /(y^2-x^2)
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