Certain ODEs can be simplified into basic linear ODEs or separable ODEs via substitution.
Homogenous Type First Order ODEs
A first order homogenous ODE is one of the form: First order homogenous ODEs can be simplified by using a substitution of . Note that since a change of variable has occurred, we need to derive (via the Product rule).
Warning not the same as as a homogenous ODE in higher power ODEs.
Note that this is
1: Homogenous ODE
Solve the following ODE:
Let Then (Product Rule) Subbing back into original equation:
Bernoulli’s Equation
#todo Which equation exactly?
The equation has the form: By substituting , the equation can be reduced to a linear ODE