Solve dy/dx = y^2 in TWO WAYS!! (Separation of Variables and Power Series Solution)
Consider the first order ODE dy/dx = y' = y^2. We first solve it using separation of variables (also emphasizing why separation of variables works). Then we draw the slope field and solution graphs, emphasizing that the equilibrium point at the origin is a "node". After that, we use a power series to solve the differential equation. We get the same answer as a geometric series (and Taylor series for the solution) for an initial-value problem with y(0)=1.
Differential Equations for Calculus 2, Part 8B
#Calculus2 #DifferentialEquations #PowerSeries
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