### Linear Programming

goals
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 : $x + y \leq 4, x \geq 0, y\geq 0$