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.

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