### Linear Programming

goals
Solution of $\left ( \dfrac {x+y-a}{x+y-b} \right )\left ( \dfrac{dy}{dx} \right ) =\left ( \dfrac {x+y+a}{x+y+b} \right )$
Solution of $\left ( \dfrac {x+y-a}{x+y-b} \right )\left ( \dfrac{dy}{dx} \right ) =\left ( \dfrac {x+y+a}{x+y+b} \right )$
There are two types of fertilisers $F_{1}$ and $F_{2}\cdot F_{1}$ consists of $10$% nitrogen and $6$%phosphoric acid and $F_{2}$ consists of $5$% nitrogen and $10$% phosphoric acid. After testing the soil conditions, a farmer finds that she needs atleast $14\ kg$ of nitrogen and $14\ kg$ of phosphoric acid for her crop. If $F_{1}$ costs $Rs. 6/kg$ and $F_{2}$ costs $Rs. 5/kg$, determine how much of each type of fertiliser should be used so that nutrient requirements are met at a minimum cost. What is the minimum cost?
The solution of the differential equation $ydx+\left( x+{ x }^{ 2 }y \right) dy=0$ is
The solution of the differential equation $ydx+\left( x+{ x }^{ 2 }y \right) dy=0$ is