(dy)/(dx)=\sqrt[3]{2/9 y}

解

\frac{d y}{d x} = 3 \frac{2}{9} y

y = \frac{2 2 2 \cdot 9 ^{\frac{2}{3}} x ^{3} + 27 \cdot 2 ^{\frac{2}{3}} c _{1} x ^{2} + 27 3 18 c _{1}^{2} x + 9 \cdot 9 ^{\frac{2}{3}} c _{1}^{3}}{9 3 9 3}, y = - \frac{2 2 2 \cdot 9 ^{\frac{2}{3}} x ^{3} + 27 \cdot 2 ^{\frac{2}{3}} c _{1} x ^{2} + 27 3 18 c _{1}^{2} x + 9 \cdot 9 ^{\frac{2}{3}} c _{1}^{3}}{9 3 9 3}

解答ステップ

\frac{d y}{d x} = 3 \frac{2}{9} y

分離可能 ODE を解く:

y = \frac{2 2 2 \cdot 9 ^{\frac{2}{3}} x ^{3} + 27 \cdot 2 ^{\frac{2}{3}} c _{1} x ^{2} + 27 3 18 c _{1}^{2} x + 9 \cdot 9 ^{\frac{2}{3}} c _{1}^{3}}{9 3 9 3}, y = - \frac{2 2 2 \cdot 9 ^{\frac{2}{3}} x ^{3} + 27 \cdot 2 ^{\frac{2}{3}} c _{1} x ^{2} + 27 3 18 c _{1}^{2} x + 9 \cdot 9 ^{\frac{2}{3}} c _{1}^{3}}{9 3 9 3}

y = \frac{2 2 2 \cdot 9 ^{\frac{2}{3}} x ^{3} + 27 \cdot 2 ^{\frac{2}{3}} c _{1} x ^{2} + 27 3 18 c _{1}^{2} x + 9 \cdot 9 ^{\frac{2}{3}} c _{1}^{3}}{9 3 9 3}, y = - \frac{2 2 2 \cdot 9 ^{\frac{2}{3}} x ^{3} + 27 \cdot 2 ^{\frac{2}{3}} c _{1} x ^{2} + 27 3 18 c _{1}^{2} x + 9 \cdot 9 ^{\frac{2}{3}} c _{1}^{3}}{9 3 9 3}