(dy)/(dx)=y+y^3

解

\frac{d y}{d x} = y + y^{3}

y = \frac{e ^{2 x + 2 c_{1}}}{1 - e ^{2 (x + c_{1})}}, y = - \frac{e ^{2 x + 2 c_{1}}}{1 - e ^{2 (x + c_{1})}}

解答ステップ

\frac{d y}{d x} = y + y^{3}

分離可能 ODE を解く:

y = \frac{e ^{2 x + 2 c_{1}}}{1 - e ^{2 (x + c_{1})}}, y = - \frac{e ^{2 x + 2 c_{1}}}{1 - e ^{2 (x + c_{1})}}

y = \frac{e ^{2 x + 2 c_{1}}}{1 - e ^{2 (x + c_{1})}}, y = - \frac{e ^{2 x + 2 c_{1}}}{1 - e ^{2 (x + c_{1})}}