Differential equations (DEs) come in many varieties. And different varieties of DEs can be solved using different methods. You can classify DEs as ordinary and partial Des. In addition to this distinction they can be further distinguished by their order.

Here are some examples:

Solving a differential equation means finding the value of the dependent variable in terms of the independent variable. The following examples use y as the dependent variable, so the goal in each problem is to solve for y in terms of x.

An ordinary differential equation (ODE) has only derivatives of one variable — that is, it has no partial derivatives. Here are a few examples of ODEs:

In contrast, a partial differential equation (PDE) has at least one partial derivative. Here are a few examples of PDEs: Sharperbrain program telewizyjny.

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DEs are further classified according to their order. This classification is similar to the classification of polynomial equations by degree.

First-order ODEs contain only first derivatives. For example:

SFOPDES is a new stepwise first order partial differential equation solver. The first version (in Spanish) was aimed to be used as a tutorial for teaching a partial differential equation course for Engineering students,.

Higher-order ODEs are classified, as polynomials are, by the greatest order of their derivatives. Here are examples of second-, third-, and fourth-order ODEs:

As with polynomials, generally speaking, a higher-order DE is more difficult to solve than one of lower order.

What constitutes a linear differential equation depends slightly on who you ask. For practical purposes, a linear first-order DE fits into the following form:

where a(x) and b(x) are functions of x. Here are a few examples of linear first-order DEs:

Linear DEs can often be solved, or at least simplified, using an integrating factor.

A linear second-degree DE fits into the following form:

where a,b, and c are all constants. Here are some examples:

Note that the constant a can always be reduced to 1, resulting in adjustments to the other two coefficients.

Ordinary Differential Equations

Solves boundary-value problems involving ordinary differential equations producing a finite series valid in the entire defined interval. Handles a wide variety of functions, including trigonometric and hyperbolic.

• Publisher: Numerical Mathematics
• Home page:www.numericalmathematics.com

Engineering Equation Solver

ES (pronounced 'ease') is a general equation-solving program that can numerically solve thousands of coupled non-linear algebraic and differential equations. The program can also be used to solve differential and integral equations, do optimization, provide uncertainty analyses

• Publisher: F-Chart Software, LLC.
• Last updated: November 27th, 2017

EES (64 bit) Engineering Equation Solver

EES (pronounced 'ease') is a general equation-solving program that can numerically solve thousands of coupled non-linear algebraic and differential equations. The program can also be used to solve differential and integral equations, do optimization, provide uncertainty analyses, perform linear and non-linear regression, convert units.

• Publisher: F-Chart Software
• Last updated: May 24th, 2018

Heat Transfer

Heat Transfer Solver shows a group of Heat Transfer problems with solutions. It Solves Heat Transfer BVP, IVP, IP problems. Source code + Output files are included. The source codes are short; less then 100 lines. They were written to demonstrate Calculus (level) Programming. Calculus Programming makes solving partial differential equations, ordinary differential equations.

• Publisher: Optimal Designs Enterprise
• Home page:digitalCalculus.com
• Last updated: April 20th, 2010

Agros2D

Agros2D is a multi-platform C++ application designed for the solution of partial differential equations (PDE) based on the Hermes library. It provides features such as:- Numerical solution of physical fields (single and multi-physics analysis with the possibility of weak and hard coupling)- Complex time-dependent nonlinear solver- Steady state, harmonic and transient analysis

• Publisher: Agros2D Development Team
• Home page:www.agros2d.org
• Last updated: March 25th, 2015

Berkeley Madonna

Berkeley Madonna is arguably the fastest, most convenient, general purpose differential equation solver available today. It is relatively inexpensive and runs on both Windows and Mac OS.Developed on the Berkeley campus under the sponsorship of NSF and NIH, it is currently used by academic and commercial institutions for constructing mathematical models for research and teaching.

• Publisher: Berkeley Madoona, Inc.
• Home page:www.berkeleymadonna.com
• Last updated: March 17th, 2010

PSI-Plot

It is an application designed for technical plotting and data analysis. It has a powerful scientific spreadsheet for data analysis, and an object-oriented on screen graphics editor that makes it easy to design and modify graphs.Main Features;- powerful scientific spreadsheet.- data import from Excel, ASCII, CSV, Access, DBase, etc.

• Publisher: Poly Software International, Inc.
• Home page:www.polysoftware.com
• Last updated: April 23rd, 2013

Newton 2

Newton 2 is a program for solving mechanical equations for movements numerically. The equations can be parameterized for interactive investi-gations of the movements and the according solutions are displayed immediately in a diagram. The differential equations (DEQs) are programmed to calculate the time dependence of the velocitiy v(t) of a point of mass from the given acceleration a.

• Publisher: Vega TEAM
• Last updated: October 8th, 2010

Graphmatica

Graphmatica is a powerful, easy-to-use, equation plotter with numerical and calculus features. It provides support for Graph Cartesian functions, relations, and inequalities, plus polar, parametric, and ordinary differential equations. You can print your graphs or copy them to clipboard in bitmap or vector format in black-and-white or color.

• Publisher: Keith Hertzer, kSoft, Inc
• Home page:www.graphmatica.com
• Last updated: May 27th, 2014

Maxima

Maxima is a system for the manipulation of symbolic and numerical expressions, including differentiation, integration, Taylor series, Laplace transforms, ordinary differential equations, systems of linear equations, polynomials, and sets, lists, vectors, matrices, and tensors.

• Publisher: The Maxima Development Team
• Home page:maxima.sourceforge.net
• Last updated: August 27th, 2019

DSTool

DsTool is a program for interactively exporting the dynamics of dynamical systems. It allows you to draw trajectories, to find fixed points or bifurcation points. Dynamical systems arise in many disciplins of physics, biology and chemistry - basically always whenever something can be described by a set ordinary differential equations.

• Publisher: Mark Myers
• Home page:www.apmaths.uwo.ca
• Last updated: October 5th, 2016

FreeFem++

Problems involving PDE (2d, 3d) from several branches of physics such as fluid-structure interactions require interpolations of data on several meshes and their manipulation within one program. FreeFem++ includes a fast 2^d-tree-based interpolation algorithm and a language for the manipulation of data on multiple meshes (as a follow up of bamg).

• Publisher: FreeFem
• Last updated: May 3rd, 2012

Gepasi

Gepasi is a software package for modeling biochemical systems. It simulates the kinetics of systems of biochemical reactions and provides a number of tools to fit models to data, optimize any function of the model, perform metabolic control analysis and linear stability analysis.

• Publisher: Pedro Mendes
• Home page:www.gepasi.org
• Last updated: March 11th, 2008

Omnigraph

The Omnigraph graph processor is an indispensible tool for pupils of all ages. The software enables you to draw lines like y = x + 1 either by typing the equation or by just clicking the screen. Graphs and shapes can be transformed and manipulated on screen. Omnigraph’s features have made it the number one graphing package in UK schools.

• Publisher: Virtual Image Publishing Ltd .
• Home page:www.virtualimage.co.uk
• Last updated: March 26th, 2010

MathGrapher

MathGrapher is the mathematical graphing program specifically designed for students, scientists and engineers. With this program students can draw and analyse functions and data in 2D and 3D, draw surface graphs, contour plots and cross-sections through contour plots. The MathGrapher includes linear and nonlinear curve fitting, integration and analysis of coupled ordinary differential equations.

• Publisher: MathGrapher
• Home page:www.mathgrapher.com
• Last updated: May 20th, 2008

Formulize

Formulize or Eureka II is a program that looks and feels like a spreadsheet, but has the ability to search the data and find mathematical patterns underlying it.Features:-Discover mathematical relationships between columns of your data-Find dynamic relationships in time-series data, in the form of differential equations-Reveal other hidden patterns and invariants in your data

• Publisher: Nutonian, Inc.
• Last updated: October 14th, 2013

DYNAST for Windows

Dynamic multipole models that can be set up in DYNAST in a graphical form characterize directly the real configuration of dynamic systems. The multipole models, however, can be combined with equations and block diagrams. DYNAST not only solves nonlinear algebro-differential equations, but also automatically formulates them for the multipole models.

• Publisher: DYN
• Last updated: May 5th, 2011

shetran

SHETRAN is a model for water flow, solute and sediment transport in river catchments. It is a finite-difference model in which the physics-based governing partial differential equations for flow and transport are solved on a three-dimensional grid. SHETRAN is a physically-based, spatially-distributed (PBSD) modelling system.

• Publisher: Newcastle University
• Home page:research.ncl.ac.uk
• Last updated: August 24th, 2015