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Differential Equation Solver

Tool/solver for resolving differential equations (eg resolution for first degree or second degree) according to a function name and a variable.

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Differential Equation Solver -

Tag(s) : Functions, Symbolic Computation

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# Differential Equation Solver

## Differential Equation Calculator

Tool/solver for resolving differential equations (eg resolution for first degree or second degree) according to a function name and a variable.

### How to calculate a differential equation on dCode?

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

### What is a differential equation? (definition)

A differential equation (or equadiff) is an equation that relates an unknown function to its derivatives (of order n).

Example: g'' + g = 1

### 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.