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Differential Equation Solver

Tool/solver for resolving differential equations (eg resolution for first degree or second degree) according to a function name and a variable.

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Differential Equation Solver -

Tag(s) : Functions, Symbolic Computation

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# Differential Equation Solver

## Differential Equation Calculator

Please, respect the syntax (see questions)

 Calculate General Solution Particular Solution(s)

### How to calculate a differential equation on dCode?

The equation must follow a strict syntax to get a solution in the differential equation solver:

— Use ' to represent the derivative of order 1, ' ' for the derivative of order 2, ' ' ' for the derivative of order 3, etc.

Example: f' + f = 0

— Do not indicate the variable to derive in the diffequation.

Example: f(x) is noted f and the variable x must be specified in the variable input.

Example: $f' + f = 1 \Rightarrow f(x) = c_1 e^{-x}+1$ with $c_1$ a constant

— Only the function is differentiable and not a combination of function

Example: (1/f)' is invalid but 1/(f') is correct

### What is a differential equation? (definition)

A differential equation (or diffeq) is an equation that relates an unknown function to its derivatives (of order n).

Example: g'' + g = 1

There are homogeneous and particular solution equations, nonlinear equations, first-order, second-order, third-order, and many other equations.

### How to add initial values/conditions?

It is possible to add one or more initial conditions in the corresponding box by adding the logical operator && between 2 equations.

Example: Write f'(0)=-1 && f(1)=0

### How to find values of constants c?

Use known information about the function and its derivative(s) as the initial conditions of the system.

Example: The position of an object is $h$ at the start of an experiment, write something like $f (0) = h$

Example: Object speed is $0$ after $n$ seconds, write something like $f'(n) = 0$

### What are the notations of the differential equations?

There are multiple notations for a function f:

Example: $$f'(x) = \frac{\mathrm{d} f(x)}{\mathrm{d}x}$$

Example: $$f''(x) = \frac{\mathrm{d}^2 f(x)}{\mathrm{d}x^2}$$

The apostrophe indicates the order/degree of derivation, the letter in parenthesis is the derivation variable.

The exponent indicates the order/degree of derivation, the letter of the denominator is the derivation variable.

### How to solve a differential equation step by step?

The calculation steps of the dCode solver are not displayed because they are computer operations far from the steps of a student's process.

## Source code

dCode retains ownership of the "Differential Equation Solver" source code. Except explicit open source licence (indicated Creative Commons / free), the "Differential Equation Solver" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or the "Differential Equation Solver" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, or API access for "Differential Equation Solver" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app!
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Differential Equation Solver on dCode.fr [online website], retrieved on 2023-09-27, https://www.dcode.fr/differential-equation-solver

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