(dy)/(dx)=(1+y^2)/((1+x^2)xy)

解

\frac{d y}{d x} = \frac{1 + y ^{2}}{( 1 + x ^{2} ) x y}

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

解答ステップ

\frac{d y}{d x} = \frac{1 + y ^{2}}{( 1 + x ^{2} ) x y}

分離可能 ODE を解く:

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

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