Solving a Basic Piecewise Defined DE with Initial Conditions

I am going to attempt to explain how to solve a piecewise defined DE that has some intial conditions. In this lecture, we will solve using an “in situ” format in order to keep the problem writing / rewriting to  a minimum. and I will detail how to find both of the arbitrary constant values being only given one condition. I hope the method or ideas posed in this lecture care helpful to understanding this type of problem. Enjoy!

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