## anonymous 5 years ago 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?

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}$