(dy)/(dx)=(4(1-y)^2)/((1-2x)^2)

解

\frac{d y}{d x} = \frac{4 ( 1 - y ) ^{2}}{( 1 - 2 x ) ^{2}}

y = \frac{2 c _{1} x}{- 2 + 2 c _{1} x - c _{1}} - \frac{2 x}{- 2 + 2 c _{1} x - c _{1}} - \frac{c _{1}}{- 2 + 2 c _{1} x - c _{1}} - \frac{1}{- 2 + 2 c _{1} x - c _{1}}

解答ステップ

\frac{d y}{d x} = \frac{4 ( 1 - y ) ^{2}}{( 1 - 2 x ) ^{2}}

分離可能 ODE を解く:

y = \frac{2 c _{1} x}{- 2 + 2 c _{1} x - c _{1}} - \frac{2 x}{- 2 + 2 c _{1} x - c _{1}} - \frac{c _{1}}{- 2 + 2 c _{1} x - c _{1}} - \frac{1}{- 2 + 2 c _{1} x - c _{1}}

y = \frac{2 c _{1} x}{- 2 + 2 c _{1} x - c _{1}} - \frac{2 x}{- 2 + 2 c _{1} x - c _{1}} - \frac{c _{1}}{- 2 + 2 c _{1} x - c _{1}} - \frac{1}{- 2 + 2 c _{1} x - c _{1}}