Differential equation calculator with initial condition | Ordinary differential equations

Differential equation calculator

(Enter the differential equation)
Solve for ( )

x0   y(x0) 

Differential equation:


The Ordinary Differential Equations Calculator that we are pleased to put in your hands is a very useful tool when it comes to studying and solving differential equations.

Its intuitive interface means that you can use it from the first moment without having to spend time reading the instructions for use. But so that you do not have any doubts about how to use the differential equation calculator, we will explain step by step how to use it below. In turn, after the introduction we will show you a brief introduction to the most relevant theoretical concepts in the world of ordinary differential equations.

Instructions for using the differential equation calculator

  1. The first step in using the calculator is to indicate the variables that define the function that will be obtained after solving the differential equation. To do so, the two fields at the top of the calculator will be used. For example, if you want to solve the second-order differential equation y”+4y’+ycos(x)=0, you must select the variables y , x as shown in the following image:
  1. In the second step, the differential equation to be solved is entered. To do this, you must write the expression in the main field of the calculator, either using the keyboard of the calculator itself or that of your device. Note that you must use single quotes, and’, to indicate the first derivative, two single quotes to indicate the second derivative, etc.
  1. If it is required to solve the differential equation from certain initial conditions, you must press the blue button below the keyboard. When doing so, a box will be displayed with those necessary to enter the initial conditions. It is important to note that you can enter them directly in the main field, separating each condition with a comma, for example: y”+4y’+ycos(x)=0, y(1)=2.
  2. Finally, you just have to press the «Calculate» button and a window with the solution will automatically be displayed, as shown below:
ordinary differential equation calculator

What are differential equations?

Differential equations are mathematical equations that describe how a quantity changes as a function of one or more (independent) variables, often over time or space. We can also define a differential equation as an equation composed of a function and its derivatives.

A differential equation is one that is written in the form y’ = ………. Some differential equations can be solved simply by performing integration, while others require much more complex mathematical processes.

What is order of differential equation?

The order of a differential equation is determined by the highest order derivative. The higher the order of the differential equation, the more arbitrary constants must be added to the general solution. A first-order equation will have one, a second-order equation will have two, and so on. A particular solution can be found by assigning values to the arbitrary constants to match any given constraint.

Degree of differential equation

The degree of a differential equation is determined by the highest power in one of its variables.

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