Wronskian[{y1,y2,…},x]
gives the Wronskian determinant for the functions y1,y2,… depending on x.
Wronskian[eqn,y,x]
gives the Wronskian determinant for the basis of the solutions of the linear differential equation eqn with dependent variable y and independent variable x.
Wronskian[eqns,{y1,y2,…},x]
gives the Wronskian determinant for the system of linear differential equations eqns.


Wronskian
Wronskian[{y1,y2,…},x]
gives the Wronskian determinant for the functions y1,y2,… depending on x.
Wronskian[eqn,y,x]
gives the Wronskian determinant for the basis of the solutions of the linear differential equation eqn with dependent variable y and independent variable x.
Wronskian[eqns,{y1,y2,…},x]
gives the Wronskian determinant for the system of linear differential equations eqns.
Examples
open all close allBasic Examples (3)
Scope (9)
Functions (6)
Applications (2)
Properties & Relations (5)
Wronskian is equivalent to a determinant:
Wronskian detects linear dependence:
Casoratian performs linear dependence for sequences of a discrete argument:
Use Orthogonalize to generate a set of linearly independent functions:
Express a function in terms of the basis:
The last component is linearly dependent on the previous ones:
Use Reduce to express polynomials and rational functions in terms of each other:
See Also
Related Guides
History
Text
Wolfram Research (2008), Wronskian, Wolfram Language function, https://reference.wolfram.com/language/ref/Wronskian.html.
CMS
Wolfram Language. 2008. "Wronskian." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Wronskian.html.
APA
Wolfram Language. (2008). Wronskian. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Wronskian.html
BibTeX
@misc{reference.wolfram_2025_wronskian, author="Wolfram Research", title="{Wronskian}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/Wronskian.html}", note=[Accessed: 11-August-2025]}
BibLaTeX
@online{reference.wolfram_2025_wronskian, organization={Wolfram Research}, title={Wronskian}, year={2008}, url={https://reference.wolfram.com/language/ref/Wronskian.html}, note=[Accessed: 11-August-2025]}