Frobenius Method Calculator: Step-by-Step Solutions

Indicial equation, the three cases, recurrence and Frobenius series. Every step of the solution is shown, as you would write it on paper, using exact fractions.

What it solves

Solve $x^2{y}^{\prime \prime }+xP(x)y^{\prime }+Q(x)y=0$ near $x=0$ with $y=\sum a_n{x}^{n+r}$, where $P$ and $Q$ are polynomials. Bessel's equation of order $\nu$ is $P=1$, $Q=x^2-{\nu }^2$.

How to use it

1. Enter your own numbers or functions in the boxes (an example is already filled in, or press Random example).
2. Check the equation preview, then press Solve step by step.
3. Reveal the solution one step at a time with Next step, or show everything at once.

Need the theory first? Read Section 6.2: Solutions About Singular Points: The Frobenius Method, which explains the method in small steps with worked examples and exercises, then come back and test yourself with the Chapter 6 quiz.

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