### Linear Programming

goals
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 $\dfrac{dy}{dx} = \dfrac{\sqrt{1 - y^2}}{y}$.