Wronskian Calculator
Work out wronskian instantly with clear inputs, formula shown and shareable results.
About Wronskian Calculator
The Wronskian is the determinant of the matrix of functions and their derivatives. For solutions of a linear ODE, a non-zero Wronskian anywhere proves linear independence and confirms a complete solution basis.
Formula
Wronskian
W(f₁, f₂) = f₁·f₂' − f₂·f₁'
Worked example
With the default values below, Wronskian Calculator returns Wronskian W = f₁f₂' − f₂f₁' of -1.00000000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- f₁ at the point
- 1
- f₁' at the point
- 2
- f₂ at the point
- 3
- f₂' at the point
- 5
Results
- Wronskian W = f₁f₂' − f₂f₁'
- -1.00000000
- Interpretation
- Non-zero Wronskian — the functions are linearly independent
- f₁·f₂'
- 5.00000000
- f₂·f₁'
- 6.00000000
Step by step
- 1Values used
- 2Wronskian
- 3Wronskian W = f₁f₂' − f₂f₁'= -1.00000000
- 4Interpretation= Non-zero Wronskian — the functions are linearly independent
- 5f₁·f₂'= 5.00000000
- 6f₂·f₁'= 6.00000000
Assumptions and limits
- The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
With f₁ = 1, f₁' = 2, f₂ = 3, f₂' = 5?
W = 5 − 6 = −1, non-zero, so the two functions are independent at that point.
Does a zero Wronskian prove dependence?
Not in general, but it does for solutions of the same linear ODE, thanks to Abel's identity.