(xy^')/(y-2)=y^2-y

解

\frac{x y ^{^{'}}}{y - 2} = y^{2} - y

y = \frac{x ^{2} - c _{1}^{2} + c _{1} - x ^{2} + c _{1}^{2}}{x ^{2} - c _{1}^{2}}, y = \frac{x ^{2} - c _{1}^{2} - c _{1} - x ^{2} + c _{1}^{2}}{x ^{2} - c _{1}^{2}}

解答ステップ

\frac{x y ^{'} ( x )}{y - 2} = y^{2} - y

線形 ODE を解く:

y = \frac{x ^{2} - c _{1}^{2} + c _{1} - x ^{2} + c _{1}^{2}}{x ^{2} - c _{1}^{2}}, y = \frac{x ^{2} - c _{1}^{2} - c _{1} - x ^{2} + c _{1}^{2}}{x ^{2} - c _{1}^{2}}

y = \frac{x ^{2} - c _{1}^{2} + c _{1} - x ^{2} + c _{1}^{2}}{x ^{2} - c _{1}^{2}}, y = \frac{x ^{2} - c _{1}^{2} - c _{1} - x ^{2} + c _{1}^{2}}{x ^{2} - c _{1}^{2}}