Wronskian Calculator
Free online wronskian calculator. Enter your values and get instant results with the formula, step-by-step working, a worked example and FAQs — everything runs locally in your browser on Calcton, no signup required.
中文版：朗斯基行列式计算器
二阶线性常系数方程 y″ + p·y′ + q·y = 0：由特征根构造两个解 y₁、y₂，计算朗斯基行列式 W(x) = y₁·y₂′ − y₁′·y₂。W ≠ 0 说明两解线性无关，通解 y = C₁y₁ + C₂y₂。
Abel 恒等式：W(x) = W(0)·e^(−p·x)，因此 W 要么恒为零要么处处非零。实根情形 W(0) = r₂ − r₁；复根 r = α ± βi 情形 W = β·e^(2αx) = β·e^(−p·x)（因 2α = −p），恒不为零。只有重根（p² = 4q）时两解退化为同一指数函数，第二个解须改取 x·e^(rx)。
How to use the Wronskian Calculator
- Fill in the inputs with your own numbers — every field shows what it expects.
- The result updates instantly as you type; no "Calculate" click needed.
- Read the result card for the main figure, the step-by-step formula, and practical notes.
Frequently asked questions
Is the Wronskian Calculator free?
Yes — all math calculators on Calcton are free, with no sign-up required. Your inputs are processed in your browser and never sent to a server.
Is there a Chinese version of this tool?
Yes. Use the Chinese version link above — it is the same calculator with the interface in Simplified Chinese.
References
Formulas and benchmarks used by this calculator follow these published sources.
KevinContent LeadCalcton Editorial Team · Last updated 2026-09-12
Kevin maintains Calcton's formula verification and content: every calculator cites the standard it implements, worked examples are recomputed programmatically, and health benchmarks follow WHO and international guidelines.
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