Use mclaughlin formula, the first term of numerator and the first three terms of denominator.

The original formula = lim (x→ 0) {x 3/[x-(x-x 3/6)]} = 6.

xy'-y=0

= & gty'=y/x

= & gtdy/y=dx/x

= & gtln|y|=ln|x|+lnC

= & gtY=Cx, and the symbol after removing the absolute value is included in C.

or

Xy'-y=0, that is, (xy'-y)/y 2 = 0, that is, (y/x)'=0.

y/x=C

y=cx

Extended data:

Let f(x) r > be the convergence radius of McLaughlin series; 0, when n→∞, if the n-order derivative f(n)(x) of the function f(x) at any fixed point x is bounded, the function f(x) can be expanded into a McLaughlin series in the convergence interval (-R, r).

Formula (2) is usually called maclaurin expansion of f(x) or power series expansion of f(x) when x=0. In formula (2), the series at the right end of the sign is called McLaughlin series of f(x) or expanded into a power series of x.

Baidu Encyclopedia-McLaughlin Formula