Tool/solver for resolving differential equations (eg resolution for first degree or second degree) according to a function name and a variable.
Differential Equation Solver - dCode
Tag(s) : Functions, Symbolic Computation
dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!
Differential Equation Solver
Differential Equation Calculator
Answers to Questions (FAQ)
What is a differential equation? (Definition)
A differential equation (or differential equation) is a mathematical equation relating a function to one or more of its derivatives (with respect to the same variable).
There are different types of differential equations: linear or nonlinear, homogeneous or nonhomogeneous, with constant or variable coefficients, first-order, second-order, third-order equations, and many others.
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 ′ (single quote) 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
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
What is the difference between a general solution and a particular solution?
The general solution of a differential equation encompasses all possible solutions and contains one or more constants of integration, denoted $ c $.
The particular solution is obtained by assigning specific values to these constants, usually using initial conditions or physical constraints.
Sometimes, dCode cannot determine the general solution but can calculate one or more particular solutions.
How to find values of constants c?
Use the known information about the function or its derivatives, called initial conditions or boundary conditions.
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 intermediate calculation steps are not displayed by the dCode solver because the solution relies on complex symbolic and numerical algorithms, very different from a classic manual solution required of a student.
Source code
dCode retains ownership of the "Differential Equation Solver" source code. Any algorithm for the "Differential Equation Solver" algorithm, applet or snippet or script (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or any "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.) or any database download or API access for "Differential Equation Solver" or any other element are not public (except explicit open source licence). Same with the download for offline use on PC, mobile, tablet, iPhone or Android app.
Reminder: dCode is an educational and teaching resource, accessible online for free and for everyone.
Cite dCode
The content of the page "Differential Equation Solver" and its results may be freely copied and reused, including for commercial purposes, provided that dCode.fr is cited as the source (Creative Commons CC-BY free distribution license).
Exporting the results is free and can be done simply by clicking on the export icons ⤓ (.csv or .txt format) or ⧉ (copy and paste).
To cite dCode.fr on another website, use the link:
In a scientific article or book, the recommended bibliographic citation is: Differential Equation Solver on dCode.fr [online website], retrieved on 2025-12-18,
- Differential Equation Calculator
- What is a differential equation? (Definition)
- How to calculate a differential equation on dCode?
- How to add initial values/conditions?
- What is the difference between a general solution and a particular solution?
- How to find values of constants c?
- What are the notations of the differential equations?
- How to solve a differential equation step by step?
