Question

Question attached as screenshot below: I am following along diligently, please help me.

Answer 1

To solve this problem, we have to use implicit derivation. To do it, derive each expression as usual and multiply by y' each expression that contains y, this way:

`\begin{gathered} 4+xy=y^2 \\ y+xy^(\prime)=2yy^(\prime) \end{gathered}`

Now, solve the obtained equation for y':

`\begin{gathered} xy^(\prime)-2yy^(\prime)=-y \\ y^(\prime)(x-2y)=-y \\ y^(\prime)=-(y)/(x-2y) \\ (dy)/(dx)=-(y)/(x-2y) \end{gathered}`