(dy)/(dx)=(4y^{3/4})/(x^2+1)

解

\frac{d y}{d x} = \frac{4 y ^{\frac{3}{4}}}{x ^{2} + 1}

y = arctan^{4} (x) + c_{1} arctan^{3} (x) + \frac{3 c _{1}^{2} arctan ^{2} ( x )}{8} + \frac{c _{1}^{3} arctan ( x )}{16} + \frac{c _{1}^{4}}{256}

解答ステップ

\frac{d y}{d x} = \frac{4 y ^{\frac{3}{4}}}{x ^{2} + 1}

分離可能 ODE を解く:

y = arctan^{4} (x) + c_{1} arctan^{3} (x) + \frac{3 c _{1}^{2} arctan ^{2} ( x )}{8} + \frac{c _{1}^{3} arctan ( x )}{16} + \frac{c _{1}^{4}}{256}

y = arctan^{4} (x) + c_{1} arctan^{3} (x) + \frac{3 c _{1}^{2} arctan ^{2} ( x )}{8} + \frac{c _{1}^{3} arctan ( x )}{16} + \frac{c _{1}^{4}}{256}