This Wronskian calculator will help you determine the linear independence of a set of functions quickly and accurately.

## About This Wronskian Calculator

This calculator allows you to determine the Wronskian of two functions at a certain point. The Wronskian is a method used in the study of differential equations to determine whether two solutions are linearly independent.

## How to Use the Wronskian Calculator

- Enter the first function
*f(x)*in the ‘f(x)’ field. - Enter the second function
*g(x)*in the ‘g(x)’ field. - Enter the x value for which you want to calculate the Wronskian in the ‘x’ field.
- Click the ‘Calculate’ button to get the result.

## How the Calculator Works

The calculator takes the functions you input and calculates their derivatives at the point specified. It then applies the formula for the Wronskian:

**W(f, g)(x) = f(x) g'(x) – g(x) f'(x)**

It calculates the derivative numerically using the symmetric difference quotient method, for a small h value.

## Limitations

This calculator works only for functions for which JavaScript’s `eval()`

method (wrapped in the `Function`

constructor for better safety) can determine a real numerical result. Functions that involve limits, discontinuities, or are undefined at the given x value may not work correctly. Additionally, since it uses numerical derivatives, highly oscillating functions or functions with sharp turns may not yield precise derivatives, affecting the Wronskian’s accuracy.