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Back to Singular points and the method of Frobenius

Exercise 101

Avg difficulty 2.5

In the following equations classify the point x=0x=0 as ordinary, regular singular, or singular but not regular singular.

  1. y′′+y=0y''+y=0
  2. x3y′′+(1+x)y=0x^3y''+(1+x)y=0
  3. xy′′+x5y′+y=0xy''+x^5y'+y=0
  4. sin⁡(x)y′′−y=0\sin(x)y''-y=0
  5. cos⁡(x)y′′−sin⁡(x)y=0\cos(x)y''-\sin(x)y=0

Lebl, Notes on Diffy Qs, §7.3 Singular points and the method of Frobenius, exercise 101

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Adapted from Notes on Diffy Qs © 2008–2026 Jiří Lebl. Licensed under CC BY-SA 4.0. Source: Notes on Diffy Qs: Differential Equations for Engineers. Imported at revision 658bcae.