何れも y =xu と置けばよい。
y' = u + xu' となる。
(1)
y' = 2(\(\frac{y}{x}\))/(1 - (\(\frac{y}{x}\)\()^{2}\)) = 2u/(1 - \(u^{2}\))
u + xu' = 2u/(1 - \(u^{2}\))
xu' = (2u - u + \(u^{2}\))/(1 - \(u^{2}\)) = (u + \(u^{2}\))/(1 - \(u^{2}\))
= u(1 + u)/((1 - u)(1 + u) = u/(1 - u)
∫(1 - u)d\(\frac{u}{u}\) = ∫d\(\frac{x}{x}\)
log (Cx) = ∫(\(\frac{1}{u}\) - 1) du = log u - u
log (Cx) = logy - log x - \(\frac{y}{x}\), C は任意の定数。

(2)
2(\(\frac{y}{x}\))y' = -1 + (\(\frac{y}{x}\)\()^{2}\)
2u(u + xu') = -1 + \(u^{2}\)
u + xu' = (u - \(\frac{1}{u}\))/2
xu' = (u - \(\frac{1}{u}\) - 2u)/2 = -(u + \(\frac{1}{u}\))/2 = -(\(u^{2}\) + 1)/(2u)
-∫2udu/(\(u^{2}\) + 1) = ∫d\(\frac{x}{x}\)
-log(\(u^{2}\) + 1) = log(Cx)
1/((\(\frac{y}{x}\)\()^{2}\) + 1) = Cx
\(x^{2}\)/(\(x^{2}\) + \(y^{2}\)) = Cx, C は任意の定数。