y^'-y=y^3

解

y^{^{'}} - y = y^{3}

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

解答ステップ

y^{'} (t) - y = y^{3}

分離可能 ODE を解く:

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

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