goals

Solution of $$\left ( \dfrac {x+y-a}{x+y-b} \right )\left ( \dfrac{dy}{dx} \right ) =\left ( \dfrac {x+y+a}{x+y+b} \right )$$

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