Ordinary Differential Equations:Cheat Sheet/Few Useful Definitions

From Wikibooks, open books for an open world
Jump to navigation Jump to search

Wronskian of Two Functions[edit]

Definition[edit]

Wronskian of two functions, is given by

Useful Facts[edit]

  • If two functions are linearly dependent in an interval, then it's Wronskian vanishes in that interval.

Laplace Transforms[edit]

Definition[edit]

Properties[edit]

  1. for .
  2. If , then
  3. Similarly,

Laplace Transform of Few Simple Functions[edit]

Convolution[edit]

Definition[edit]

Properties[edit]

  1. Associative
  2. Commutative
  3. Distributive over addition

First Order Ordinary Differential Equations