Exercise

1. Find the general solution of the following differential equations.
$$\begin{array}{ll} (a) \ y^{\prime} = \frac{xy}{x^{2}+y^{2}} &... ...{x+2y+7} & (f) \ y^{\prime} = \frac{x-y+8}{y-3x+2} \end{array}$$
2. Solve the initial value problems.
$(a) \ (y - \sqrt{x^{2}+y^{2}})dx - xdy = 0, \ y(\sqrt{3}) = 1$
$(b) \ (y^{3}-x^{3})dx - xy^{2}dy = 0, \ y(1) = 2$
3. Give a reason why the example 1.8 can not be solved by the technique shown in example 1.7.