Differential Equation Solver

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

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.

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

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.