MATH 1005 Study Guide - Final Guide: Frobenius Method, Scilab

• School: Carleton University
• Department: Mathematics
• Course: MATH 1005
• Professor: Zahra Montazeri

Document Summary

To solve the equation (with a, b, and c constants), let y = erx. This yields the indicial equation ay00 + by0 + cy = 0. There are three cases: ar2 + br + c = 0. Then the general solution is y = c1er1 x + c2er2 x. Case 2 : the indicial equation has one repeated real solution r. then the general solution is y = c1erx + c2xerx. Then the general solution is y = c1e x cos( x) + c2e x sin( x) = e x (c1 cos( x) + c2 sin( x)) . To solve the equation ax2y00 + bxy0 + cy = 0 (with a, b, and c constants), consider x > 0 and let y = xr. There are three cases: ar(r 1) + br + c = 0. Case 1 : the indicial equation has two distinct real solutions r1 and r2. Then the general solution is y = c1|x|r1 + c2|x|r2.