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CSS Applied Mathematics QUESTION #4147
Question 1
For $(x^2+1)y'' + xy' - y = 0$, what is the indicial equation at the ordinary point $x = 0$ for power series solution?
  • $r(r-1) = 0$
  • $r^2 - 1 = 0$✔️
  • $r^2 = 0$
  • $r^2 + r = 0$
Correct Answer Explanation
At ordinary point $x=0$, substitute $y = \sum a_n x^n$. The indicial equation comes from lowest power: coefficient of $x^0$ gives $a_0$ terms. Actually for ordinary points, we get recurrence. The indicial equation for this equation at $x=0$ is $r^2 - 1 = 0$ giving $r = \pm 1$.