In Exercises 1 to 8, match each graph in a. through h. with the proper quadratic function. f(x) = (x + 1)2 + 3

Math246 Lecture 3: Separable Equations This is our first look at nonlinear first order differential equations. Separable equations take the dy form P (y)dx=W (x) . Solving these equations is fairly straightforward. We will take a 3 step approach. 1. Rewrite into the form P(y)dy=W (x)dx 2. Integrate both sides: P y dy= W(x)dx ∫ ( ) ∫ 3. Solve for the general or explicit solution. There’s not much left to say except let’s work through a few examples, so let’s work through a few examples! Examples dy 3 1. Solve =7x y dx Ok, first we move everything into place. 1 3 dy=7x dx