{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lesson 4a - Homogeneous

# Lesson 4a - Homogeneous - y y f x y u x xu y...

This preview shows pages 1–3. Sign up to view the full content.

Homogenous First Order ODEs y Consider a first order ODE that looks like the following: ) ( ' x f y Then we could substitute: y u x y xu Deriving implicitly with respect to x implicitly will yield (do not forget product rule!): ' ' y xu u This gives us the following differential equation instead: ) ( ' u f xu u u u f xu ) ( ' ' 1 x u u u f 1 ' ) ( 1 This is a separable equation! Provided that we 1 ) ( xu u u f can integrate both sides, we will be able to solve this ODE rather quickly!

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Recognizing Homogenous Equations y Isolate for y’, and if you notice a few kicking around, then you can try using the homogenous strategy outlined below: x 1. Substitute and if all of your y variables disappear (and you only have the x in front of the u’ in your equation), then this will be a separable equation most definitely. x y u ' ' y xu u 2. Solve the separable equation in terms of u, u’, and x.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 5

Lesson 4a - Homogeneous - y y f x y u x xu y...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online