Enter the values of the functions in the Wronskian calculator to find their determinant and check their linear independency.
There is only one step to use this calculator: enter the functions and click calculate.
The Wronskian is named after the Polish mathematician Józef Hoene-Wroński. It is a mathematical method used to check if a set of functions is linearly dependent or independent. It involves a determinant that encompasses the functions and their derivatives.
If the Wronskian's value is zero within a certain range, the functions are linearly dependent; otherwise, they are linearly independent.
Given n differentiable functions f1 (x),f2 (x),…, fn (x), their Wronskian W is defined as the determinant of the n×n matrix whose ith row consists of the i−1th derivatives of the functions:
Given two functions y1 (x) and y2 (x):
Mathematically, the Wronskian W(y1,y2) is:
Let’s determine the Wronskian of e^x and xe^x.
Step 1: Write the given functions.
y1 = e^x
y2 = xe^x
Step 2: Calculate the first derivatives.
y1’ = e^x
y2’ = (x+1) e^x
Step 3: Construct the matrix.
Step 4: Evalvulate the determinant.
= e^x (xe^x + e^x) - xe^x (e^x)
= e^2x - xe^2x + xe^2x