y^'=\sqrt[3]{y/(x-1)}

解

y^{^{'}} = 3 \frac{y}{x - 1}

y = \frac{27 x ^{2} - 54 x + 27 + 54 c _{1} ( x - 1 ) ^{\frac{4}{3}} + 36 c _{1}^{2} ( x - 1 ) ^{\frac{2}{3}} + 8 c _{1}^{3}}{3 3}, y = - \frac{27 x ^{2} - 54 x + 27 + 54 c _{1} ( x - 1 ) ^{\frac{4}{3}} + 36 c _{1}^{2} ( x - 1 ) ^{\frac{2}{3}} + 8 c _{1}^{3}}{3 3}

解答ステップ

y^{'} (x) = 3 \frac{y}{x - 1}

分離可能 ODE を解く:

y = \frac{27 x ^{2} - 54 x + 27 + 54 c _{1} ( x - 1 ) ^{\frac{4}{3}} + 36 c _{1}^{2} ( x - 1 ) ^{\frac{2}{3}} + 8 c _{1}^{3}}{3 3}, y = - \frac{27 x ^{2} - 54 x + 27 + 54 c _{1} ( x - 1 ) ^{\frac{4}{3}} + 36 c _{1}^{2} ( x - 1 ) ^{\frac{2}{3}} + 8 c _{1}^{3}}{3 3}

y = \frac{27 x ^{2} - 54 x + 27 + 54 c _{1} ( x - 1 ) ^{\frac{4}{3}} + 36 c _{1}^{2} ( x - 1 ) ^{\frac{2}{3}} + 8 c _{1}^{3}}{3 3}, y = - \frac{27 x ^{2} - 54 x + 27 + 54 c _{1} ( x - 1 ) ^{\frac{4}{3}} + 36 c _{1}^{2} ( x - 1 ) ^{\frac{2}{3}} + 8 c _{1}^{3}}{3 3}