(dy)/(dt)=-\sqrt[3]{y}

解

\frac{d y}{d t} = - 3 y

y = \frac{2 2 - t ^{3} + c _{1}^{3} + 3 c _{1} t ^{2} - 3 c _{1}^{2} t}{3 3}, y = - \frac{2 2 - t ^{3} + c _{1}^{3} + 3 c _{1} t ^{2} - 3 c _{1}^{2} t}{3 3}

解答ステップ

\frac{d y}{d t} = - 3 y

分離可能 ODE を解く:

y = \frac{2 2 - t ^{3} + c _{1}^{3} + 3 c _{1} t ^{2} - 3 c _{1}^{2} t}{3 3}, y = - \frac{2 2 - t ^{3} + c _{1}^{3} + 3 c _{1} t ^{2} - 3 c _{1}^{2} t}{3 3}

y = \frac{2 2 - t ^{3} + c _{1}^{3} + 3 c _{1} t ^{2} - 3 c _{1}^{2} t}{3 3}, y = - \frac{2 2 - t ^{3} + c _{1}^{3} + 3 c _{1} t ^{2} - 3 c _{1}^{2} t}{3 3}