First-order Substitution Methods: Bernouilli and Homogeneous ODE's.

June 1, 2019

Change of Variables

Two kinds of equations that can generally be solved is either the separable equations or the standard first order linear ODE we’ve learned last time. All the others will be solved by changing variables to reduce them to these two kinds of equations.

Why?

units;

make variables dimensionless(w/o any units)

Ex. k, M, units

Direct

Inverse, old or new variable is on the left

Ex. Bernoulli Equation

Step..

Ex. Homogeneous first order ODE’s = Invariant under zoom; inverse substitution

Arctan integral proof; Polar coordinates