x^'=x^{4/5}

解

x^{^{'}} = x^{\frac{4}{5}}

x = \frac{t ^{5}}{3125} + \frac{c _{1} t ^{4}}{625} + \frac{2 c _{1}^{2} t ^{3}}{625} + \frac{2 c _{1}^{3} t ^{2}}{625} + \frac{c _{1}^{4} t}{625} + \frac{c _{1}^{5}}{3125}

解答ステップ

x^{'} (t) = x^{\frac{4}{5}}

分離可能 ODE を解く:

x = \frac{t ^{5}}{3125} + \frac{c _{1} t ^{4}}{625} + \frac{2 c _{1}^{2} t ^{3}}{625} + \frac{2 c _{1}^{3} t ^{2}}{625} + \frac{c _{1}^{4} t}{625} + \frac{c _{1}^{5}}{3125}

x = \frac{t ^{5}}{3125} + \frac{c _{1} t ^{4}}{625} + \frac{2 c _{1}^{2} t ^{3}}{625} + \frac{2 c _{1}^{3} t ^{2}}{625} + \frac{c _{1}^{4} t}{625} + \frac{c _{1}^{5}}{3125}