Exercise

1. Solve the following differential equations, where $p = \frac{dy}{dx}$.
$$\begin{array}{ll} (a) \ p^2 - y^2 = 0 & (b) \ p^2 - 5p + 6 = ... ...ac{y^2}{x^2})p - 2(2y -x^2 - \frac{y^2}{x^2}) = 0 & \end{array}$$
2. Solve the following differential equations, where $p = \frac{dy}{dx}$.
$$\begin{array}{ll} (a) \ 2x^3 = x^4p + p^3 & (b) \ y + p^2 - 5... ...= 0 & (d)\ y = xp + \log{p^2}\\ (e)\ x^2 = 1 + p^2 \end{array}$$