Using Mathematica for ODEs, Part 6 (using DSolveValue, Manipulate, VectorPlot, pure functions)

Using Mathematica for ODEs, Part 6. Main Example: dy/dt = y^2, y(0) = y0. Using a new command for Mathematica 10 and beyond: DSolveValue...thanks go to David Arnold from the College of the Redwoods for pointing this out to me. A brief discussion of Function and pure functions. More use of Manipulate, Show, VectorPlot, and Plot, to animate graphs of solutions in slope fields. Using Exclusions to rid graphs of vertical asymptotes and PlotRange along with All to plot graphs more fully in some situations.

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