We saw that first order linear equations are differential equations in the form dy/dx+P(x)y=Q(x). In contrast, first order separable differential equations are equations in the form N(y)(dy/dx)=M(x) or N(y)y'=M(x). We call these “separable” equations because we can separate the variables onto opposite sides of the equation. In other words, we can put the x terms on the right and the y terms on the left, or vice versa, with no mixing.
Read MoreWe already know how to separate variables in a separable differential equation in order to find a general solution to the differential equation. When we’re given a differential equation and an initial condition to go along with it, we’ll solve the differential equation the same way we would normally, by separating the variables and then integrating. The constant of integration C that’s left over from the integration is the value we’ll be able to solve for using the initial condition.
Read MoreThe population of a species that grows exponentially over time can be modeled by P(t)=Pe^(kt), where P(t) is the population after time t, P is the original population when t=0, and k is the growth constant.
Read MoreWe need to change the current equation so that it's in terms of a new variable u and its derivative u'.
Read More
