(x-xy^2)dx+(y-x^2y)dy=0

解

(x - x y^{2}) d x + (y - x^{2} y) d y = 0

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

解答ステップ

(x - x y^{2}) d x + (y - x^{2} y) d y = 0

分離可能 ODE を解く:

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

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