Question

Apply separation of variables to find a solution to: (dy/dx) = r*y, where y is population size that increases at a rate proportional to its size?

Answer 1

If you multiply both sides by dx and then divide both sides by y you will have separated the variables.\[(1/y)dy=rdx\]\[\int\limits_{}^{}(1/y)dy=\int\limits_{}^{}(r)dx\]\[\ln (y) = rx + C\]\[y=e ^{rx}e ^{C}=ce ^{rx}\]