演習問題

1. 次の多項式形の微分方程式を解け．ただし, $p = \frac{dy}{dx}$．
$$\begin{array}{ll} (a) \ p^2 - y^2 = 0 & (b) \ p^2 - 5p + 6 = ... ...\ xy(1-p^2) = (x^2 - y^2)p & (d)\ xp^2 - 2yp = x\\ \end{array}$$
2. 次の微分方程式を解け．ただし, $p = \frac{dy}{dx}$.
$$\begin{array}{ll} (a) \ y = xp + 2\sqrt{p} & (b) \ y = xp - \sin p\\ (c)\ y = 2xp - p^2 & (d)\ y = xp^2 + p\\ \end{array}$$