Author Topic: non-homogeneous guessing question  (Read 729 times)

Weina Zhu

  • Jr. Member
  • **
  • Posts: 6
  • Karma: 1
    • View Profile
non-homogeneous guessing question
« on: October 08, 2018, 10:37:22 AM »
during solving the general solution for the non-homogeneous equation, why should we guessing an answer combine sin&cos together for
an equation like the right-hand side only contains one of the sin&cos.

Thanks!

Victor Ivrii

  • Administrator
  • Elder Member
  • *****
  • Posts: 2511
  • Karma: 0
    • View Profile
    • Personal website of Victor Ivrii
Re: non-homogeneous guessing question
« Reply #1 on: October 08, 2018, 01:11:46 PM »
Because derivative of sine is cosine and v.v. Try to solve $y''+y'=\cos(x)$ as with $y=a\cos(x)$.
« Last Edit: October 08, 2018, 01:35:11 PM by Victor Ivrii »