MATH 263 Study Guide - Final Guide: Integrating Factor, Talking Lifestyle 1278, Frobenius Method

• School: McGill University
• Department: Mathematics and Statistics
• Course: MATH 263
• Professor: All

Document Summary

1. (8 points) find the general solution for of the equation: (x2 + 3xy + y2) x2y = 0. Solution: this is a homogeneous equation, one has the general solution: x x + y. Q(d) = (d + 1)2 + 1 , yp = xe x cos x , y = e x(c1 cos x + c2 sin x x cos x) 4. (12 points) find the general solution for the eq. (x 1)y xy + y = sin x, (x > 1), Given that y1(x) = ex satis es the associated homogeneous eq. Solution: reduction of order gives y = x as another solution, so the general solution to the homogeneous equation is. Variation of parameters then gives yp = ux + vex where y = c1x + c2ex u = sin x. 1 x v = x sin x ex(x 1) and so the general solution is y = c1x + c2ex + xz sin x.