It’s been a while since I wrote here, and this is an attempt to resurrect the blog, and get inspiration to contribute something for Wikibooks as well.

This is a part of the book “Ordinary Differential Equations: Cheat Sheet” that I am compiling in Wikibooks, and it will be published in five instalments before/along with finalising the book in Wikibooks. And just like Examples and Counter Examples Series (Which again I am planning to compile in Wikibooks), this will also be edited as I learn.

## Wronskian of Two Functions

### Definition

Wronskian of two functions, is given by

### Useful Facts

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

## Laplace Transforms

### Definition

### Properties

- for .
- If , then
- Similarly,

### Laplace Transform of Few Simple Functions

## Convolution

### Definition

### Properties

- Associative
- Commutative
- Distributive over addition