第9章 9.29

$dx + xydy = y^2 dx + ydy$ $(1-y^2)dx = y(-x+1)dy$

$\int \frac{1}{-x+1} dx = \int \frac{y}{1-y^2} dy \quad -\log|x-1| = -\frac{1}{2}\log(1-y^2) + C_1 \quad e^{-2C_1} = C \text{ とおくと}$

$\frac{(x-1)^2}{1-y^2} = C \quad \frac{(x-1)^2}{C} + y^2 = 1 \quad C = a^2 \text{ とおくと}$

$\frac{(x-1)^2}{a^2} + y^2 = 1 \quad \text{(\text{楕円})}$