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lna + arctan(y/x)这一步是怎么取对数？
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√(x^2+y^2) = ae^[arctan(y/x)]
(1/2)ln(x^2+y^2) = lna + arctan(y/x)
(x + y.y')/(x^2+y^2) = [1/( 1+ (y/x)^2) ] .[ (xy'-y) /x^2]
= [x^2/( x^2+ y^2) ] .[ (xy'-y) /x^2]
=(xy-y')/(x^2+y^2)
x+y.y' = xy-y'
(1+y)y' = xy-x
y' = (xy-x)/(1+y)
(1/2)ln(x^2+y^2) = lna + arctan(y/x)
(x + y.y')/(x^2+y^2) = [1/( 1+ (y/x)^2) ] .[ (xy'-y) /x^2]
= [x^2/( x^2+ y^2) ] .[ (xy'-y) /x^2]
=(xy-y')/(x^2+y^2)
x+y.y' = xy-y'
(1+y)y' = xy-x
y' = (xy-x)/(1+y)
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