Differential Equation Solver

Question 1

Answer

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

Question 2

Answer

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.

Question 3

Answer

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

Question 4

Answer

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 $

Question 5

Answer

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.

Question 6

Answer

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

Differential Equation Calculator