y^'=(x-3)(y+1)^{2/3}

解

y^{^{'}} = (x - 3) (y + 1)^{\frac{2}{3}}

y = - x^{3} + \frac{x ^{6}}{216} - \frac{x ^{5}}{12} + \frac{c _{1} x ^{4}}{36} + \frac{x ^{4}}{2} + \frac{- c _{1} x ^{3} - c _{1}^{2} x}{3} + \frac{c _{1}^{2} x ^{2}}{18} + c_{1} x^{2} + \frac{c _{1}^{3}}{27} - 1

解答ステップ

y^{'} (x) = (x - 3) (y + 1)^{\frac{2}{3}}

分離可能 ODE を解く:

y = - x^{3} + \frac{x ^{6}}{216} - \frac{x ^{5}}{12} + \frac{c _{1} x ^{4}}{36} + \frac{x ^{4}}{2} + \frac{- c _{1} x ^{3} - c _{1}^{2} x}{3} + \frac{c _{1}^{2} x ^{2}}{18} + c_{1} x^{2} + \frac{c _{1}^{3}}{27} - 1

y = - x^{3} + \frac{x ^{6}}{216} - \frac{x ^{5}}{12} + \frac{c _{1} x ^{4}}{36} + \frac{x ^{4}}{2} + \frac{- c _{1} x ^{3} - c _{1}^{2} x}{3} + \frac{c _{1}^{2} x ^{2}}{18} + c_{1} x^{2} + \frac{c _{1}^{3}}{27} - 1