can this differential equation be solved using separation of variables?\n\frac{dy}{dx}=\frac{sin(y)+y}{4x +…

can this differential equation be solved using separation of variables?\n\frac{dy}{dx}=\frac{sin(y)+y}{4x + 7}\nchoose 1 answer:\na yes\nb no

can this differential equation be solved using separation of variables?\n\frac{dy}{dx}=\frac{sin(y)+y}{4x + 7}\nchoose 1 answer:\na yes\nb no

Answer

Explanation:

Step1: Recall separation - of - variables form

A first - order differential equation $\frac{dy}{dx}=f(x)g(y)$ can be solved by separation of variables.

Step2: Rewrite given equation

The given differential equation is $\frac{dy}{dx}=\frac{\sin(y)+y}{4x + 7}=\frac{1}{4x + 7}(\sin(y)+y)$. Here, $f(x)=\frac{1}{4x + 7}$ and $g(y)=\sin(y)+y$.

Answer:

A. Yes