MAT244H1 Study Guide - Integrating Factor, C Mathematical Functions, 2Zy
111 views4 pages
ultramarinemosquito394 and 14 others unlocked
11
MAT244H1 Full Course Notes
Verified Note
11 documents
Document Summary
Mat244, spring 2013, term test 1, wednesday, february 13, solutions 1. Please note: handouts are not only obligatory but allow you to solves prob- lems faster. Find integrating factor and solve x dx + y(1 + x2 + y2) dy = 0. + (y) = ey2 (1 + x2 + y2)y = xey2 x2ey2 dx + yey2. Consider equation (cos(t) + t sin(t))y t cos(t)y + y cos(t) = 0. Find wronskian w = w [y1, y2](t) of two solutions such that w (0) = 1. Check that one of the solutions is y1(t) = t. find another solution y2 such that w [y1, y2]( /2) = /2 and y2( /2) = 0. Solution. (a) consider the equation for w : W /w = t cos(t) cos(t) + t sin(t) = ln w = z t cos(t) cos(t) + t sin(t) dt = ln(cos(t) + t sin(t)) + ln c = w = c(cos(t) + t sin(t))
Get access
Grade+20% off
$8 USD/m$10 USD/m
Billed $96 USD annually
Homework Help
Study Guides
Textbook Solutions
Class Notes
Textbook Notes
Booster Class
40 Verified Answers