Power Series Solution Calculator: Step-by-Step Solutions

Recurrence relation and series solutions about an ordinary point. Every step of the solution is shown, as you would write it on paper, using exact fractions.

What it solves

Solve $p(x)y^{\prime \prime }+q(x)y^{\prime }+r(x)y=0$ with polynomial coefficients by $y=\sum a_n{x}^n$ about $x=0$ (requires $p(0)\ne 0$). Optionally give $a_0=y(0)$ and $a_1=y^{\prime }(0)$.

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 6.1: Power Series Solutions About an Ordinary Point, which explains the method in small steps with worked examples and exercises, then come back and test yourself with the Chapter 6 quiz.

All computations run in your browser; nothing is sent to a server.