Linear Programming

Find the solution of the differential equation $$\dfrac{dy}{dx} = \dfrac{\sqrt{1 - y^2}}{y}$$.
Minimize $$Z=18x+10y$$
Subject to

$$4x+y \ge 20$$
$$2x+3y \ge 30$$
Find the solution of $$\displaystyle \cos \left ( \frac{x}{y} \right )\left ( y dx-x dy \right )=xy^{3}\left ( x dy+ydx \right )$$
Find the solution of $$\displaystyle \cos \left ( \frac{x}{y} \right )\left ( y dx-x dy \right )=xy^{3}\left ( x dy+ydx \right )$$
Solve the following Linear Programming Problems graphically:
Maximise $$Z = 3x + 4y$$
subject to the constraints : $$x + y \leq 4, x \geq 0, y\geq 0$$