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
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A differential equation (or diffeq) is an equation that relates an unknown function to its derivatives (of order n).
There are homogeneous and particular solution equations, nonlinear equations, first-order, second-order, third-order, and many other equations.
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
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
The general solution of a differential equation gives an overview of all possible solutions (by integrating c constants) presented in a general form that can encompass an infinite range of solutions.
The particular solution is a particular solution, obtained by setting the constants to particular values meeting the initial conditions defined by the user or by the context of the problem.
Sometimes dCode will not be able to calculate the general solution but will be able to find one or more particular solutions.
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 $
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.
The calculation steps of the dCode solver are not displayed because they are computer operations far from the steps of a student's process.
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Cite as source (bibliography):
Differential Equation Solver on dCode.fr [online website], retrieved on 2024-12-04,