Exercise

1. Find the general solution of the following differential equations.
$$\begin{array}{ll} (a) \ (\sin{x})y^{\prime} + (\cos{x})y = 0&... ...1 - x^{2}} & (d) \ y^{\prime} = (1 + 2x)(1 + y^{2}) \end{array}$$
2. Solve the following initial value problem
$$\begin{array}{ll} (a) \ (1 + e^{x})y^{\prime} = y, \ y(0) = 1... ...rime} = \frac{x(y^2 - 1)}{(x - 1)y^{3}}, \ y(2) = 2 \end{array}$$
3. The body heated at $70^{\circ}c$ is put outside whose temparature is $20^{\circ}c$. Suppose that the temparature becomes $50^{\circ}c$ after 15 minutes
(a) Find the temparature of the body after $30$ minutes.
(b) Find the time when the body temparature becomes $32^{\circ}c$.