Differential Equation Solver

The equation must follow a strict syntax to get a solution:

- 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 from the equation.

Example: f(x) is marked 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 equadiff) is an equation that relates an unknown function to its derivatives (of order n).

Example: g'' + g = 1

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

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.