Separable Variables Differential Equations

Separable variables differential equations of first order have the following form:

As we can see, the independent variable x is totally separate from the unknown function y.

In order to solve this kind of differential equations, we integrate both sides of the equation:

First Order Linear Differential Equations

First Order Linear Differential Equations

First Order Homogeneous Linear Differential Equations

Solving First Order Linear Differential Equations

A differential equation that can be written in the following form is called first order linear differential equation:

In order to solve linear differential equations we will set:

Higher Order Linear Differential Equations with Constant Coefficients

Introduction

1st Stage: The Solution of the Homogeneous Equation

Case A: The characteristic equation has n real roots:

Case B: The characteristic equation has n multiple real roots of multiplicity q:

Case C: The characteristic equation has complex roots:

Case D: Combination of the above cases

2nd Stage: The Partial Solution

Case A: Polynomial

Case B: Exponential-Polynomial Function

Case C: Trigonometric Function

Case D: Combination of the previous cases