Linear Programming

The solution of $$ydx-xdy+\log {x}dx=0$$ is
The solution of $$ydx-xdy+\log {x}dx=0$$ is
If the point $$(2K-3,K+2)$$ lies on the graph of equation $$2x+3x+15=0$$, find the value of x.
The maximum value of $$4x+5y$$ subject to the constraints $$x+y \le 20,x+2y \le 35,x-3y \le 12$$  is
Find the solution of the differential equation $$\dfrac{dy}{dx} = \dfrac{\sqrt{1 - y^2}}{y}$$.