263_pdfsam_math 54 differential equation solutions odd

263_pdfsam_math 54 differential equation solutions odd -...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
CHAPTER 5: Introduction to Systems and Phase Plane Analysis EXERCISES 5.2: Elimination Method for Systems, page 250 1. Subtracting the second equation in the system from the Frst one, we eliminate y and obtain x 0 + y 0 = 2 y, y 0 = x 2 y x 0 = x. This equation is separable (also, it is linear). Separation yields dx x = dt ln | x | = t + C x ( t )= c 2 e t . Substituting this solution into the second equation, we obtain an equation for y : y 0 +2 y = x = c 2 e t . This equation is a Frst order linear equation. Solving we obtain µ ( t )=exp
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/29/2010 for the course MATH 54257 taught by Professor Hald,oh during the Spring '10 term at University of California, Berkeley.

Ask a homework question - tutors are online