Toronto Math Forum

MAT244--2018F => MAT244--Lectures & Home Assignments => Topic started by: Weina Zhu on October 08, 2018, 10:37:22 AM

Title: non-homogeneous guessing question
Post by: Weina Zhu 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!
Title: Re: non-homogeneous guessing question
Post by: Victor Ivrii 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 $y=a\cos(x)$.