Exercise

1. Find the general solution of the following differential equations.
$$\begin{array}{ll} (a) \ xy^{\prime} - y = -y^{2} & (b) \ xy^{... ...\ (c) \ y^{\prime} - y\cos{x} + y^{2}\cos{x} = 0 & \end{array}$$
2. Solve the following differential equations.
$$\begin{array}{ll} (a) \ yy^{\prime} + y^{2} + 4x(x+1) = 0 & (b) \ (y+1)y^{\prime} + x(y^{2} + 2y) = x \end{array}$$
3. Solve the following differential equations.
$(a) \ x^{2}y^{\prime} = -x^{2}y^{2} - 4xy -2$, provided a solution $f(x) = -2/x$
$(b) \ xy^{\prime} = y - xy^{2} + x^{3}$