what would be a step in solving the differential equation dy/dx = 3 cos(x)(y + 1)? ∫y + 1dy = ∫3 cos(x)dx…

Explanation:

Step1: Separate variables

For a first - order separable differential equation $\frac{dy}{dx}=f(x)g(y)$, we rewrite it in the form $\frac{1}{g(y)}dy = f(x)dx$. Given $\frac{dy}{dx}=3\cos(x)(y + 1)$, we divide both sides by $(y + 1)$ (assuming $y\neq - 1$) and multiply both sides by $dx$ to get $\frac{1}{y + 1}dy=3\cos(x)dx$. Then we can integrate both sides.

Answer:

$\int\frac{1}{y + 1}dy=\int3\cos(x)dx$