This calculator will help you find the Wronskian of the given set of functions, with steps shown alongside. It supports up to 5 functions, 2×2, 3×3, etc.
All you need to do is simply enter functions (comma-separated) like say cos (x), sin (x), sin (2x) and hit the calculate button. You will get the solution in no time.
In general, it is not always that easy to test whether the given set of functions is linearly independent through definition. Linear independence can however be tested with the Wronskian rule.
By definition, the Wronskian is a set of functions {z1(x)z1(x), z2z2 (x), …, zn(x)zn(x)} on the interval a≤x≤ba≤x≤b, having the property that each function possesses n-1 derivatives on this interval.
If the Wronskian of a set of n functions defined on the interval a≤x≤ba≤x≤b is non-zero for at least any one point in this interval system, then the given set of functions is said to be linearly independent there.
Although if the Wronskian is identical to zero on this interval and if each of these functions is a solution to the same linear differential equation, then the given set of functions is known to be linearly dependent.