# 2_1a - Solutions 2.1-Page 106 Problem 3 A homogeneous...

This preview shows pages 1–2. Sign up to view the full content.

Solutions 2.1-Page 106 Problem 3 A homogeneous second-order linear differential equation, two functions and , and a pair of initial conditions are given. First verify that and are solutions of the differential equation. Then find a particular solution of the form 1 y 1 + 2 y 2 y 1 y 2 y 2 1 c y c y = that satisfies the given initial conditions. Primes denote derivatives with respect to x . 0 4 = + y y ; , x y 2 cos 1 = x y 2 sin 2 = ; 3 ) 0 ( = y , 8 ) 0 ( = y The problem will first be verified for , and then the problem will be verified again for . 1 y 2 y Differentiating twice yields: 1 y x y 2 cos 4 1 = Substituting into the differential equation yields: 0 ) 2 (cos 4 2 cos 4 = + x x Differentiating twice yields: 2 y x y 2 sin 4 2 = Substituting into the differential equation yields: 0 ) 2 (sin 4 2 sin 4 = + x x The general form of the particular solution is x c x c y 2 sin 2 cos 2 1 + = . Differentiating gives x c x c y 2 sin 2 2 cos 2 1 2 = .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern