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.