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

解

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

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

解答ステップ

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

分離可能 ODE を解く:

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

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