(dy)/(dx)=(2x+xy^2)/(4y+x^2y)

解

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

y = 4 e^{2 c_{1}} + e^{2 c_{1}} x^{2} - 2, y = - 4 e^{2 c_{1}} + e^{2 c_{1}} x^{2} - 2

解答ステップ

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

分離可能 ODE を解く:

y = 4 e^{2 c_{1}} + e^{2 c_{1}} x^{2} - 2, y = - 4 e^{2 c_{1}} + e^{2 c_{1}} x^{2} - 2

y = 4 e^{2 c_{1}} + e^{2 c_{1}} x^{2} - 2, y = - 4 e^{2 c_{1}} + e^{2 c_{1}} x^{2} - 2