Wronskian Calculator: The Ultimate Linear Independence Tool
Welcome to the most advanced Wronskian Calculator available online. This free, instant tool computes the Wronskian determinant for 2 or 3 functions and determines linear independence with full step-by-step matrix construction, derivative calculation, and final verdict. Perfect for differential equations, linear algebra, and advanced calculus students worldwide.
How to Use the Wronskian Calculator
Our Wronskian Calculator is intuitive and powerful:
- Select Size: Choose 2 or 3 functions
- Enter Functions: Type f1(x), f2(x), f3(x) using standard math notation
- Set Point: Choose any x value in the domain (-1000 to 1000)
- Click Calculate: Get complete Wronskian matrix and independence result
2x2 Wronskian Calculator: Step-by-Step
For functions f(x) and g(x):
Example: sin(x), cos(x) at x = 0 → W = -1 → Independent
3x3 Wronskian Calculator: Full Determinant
For f(x), g(x), h(x):
The Wronskian Calculator computes this 3×3 determinant automatically.
Input Validation in Wronskian Calculator
- Allowed Functions: sin(x), cos(x), tan(x), e^x, ln(x), x^n, constants
- Point Range: x ∈ [-1000, 1000]
- Real-time Validation: Prevents invalid syntax
- Error Messages: Clear guidance for corrections
Supported Functions in Wronskian Calculator
- Trigonometric: sin(x), cos(x), tan(x)
- Exponential: e^x, e^(kx)
- Logarithmic: ln(x), log(x)
- Polynomials: x^3, 2x^2 + 1
- Constants: 5, π, e
When is the Wronskian Zero?
The Wronskian Calculator identifies:
- W(x) ≠0: Linearly independent on the interval
- W(x) = 0 at a point: May still be independent elsewhere
- W(x) ≡ 0: Likely linearly dependent
Applications of Wronskian Calculator
- Differential Equations: Verify fundamental solution sets
- Linear Algebra: Function space independence
- Control Theory: System observability
- Physics: Normal modes, quantum mechanics
Check Linear Independence Instantly
The most accurate Wronskian Calculator for students and researchers globally — 100% free.