A problem on x 12e x y 00 y sin2 1 associated

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

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

Unformatted text preview: sin(2 1, Associated homogeneous equation: y 00 y = 0. x 2. (a) y 000 + e =ysin(2x) x +e1) ., 1 = 0. (0) = 1 1, 1. Corresponding solutions: e x , ex y x = ln ( c) y y Roots: Auxiliary equation:2 2 Associated homogeneous equation: Notes, these are linearly independent on IR. y 00 y By Proposition 3.30 in the Course and it = 0. This equation is of 2first order, x is also linear, so both of our ExAuxiliary equation:h (x) =1c= 0x Roots:, 11. Corresponding solutions: e x , ex . + c2 e General solution: y Theorems apply. 1,Thex theorem for linear equations << 1e istence/Uniquenessin the Course Notes, these are 1. By Proposition 3.30 RHS of inhomogeneous DE: F (x) = sin(2x) 2e x linearly) independent on IR. = F1 (x + F2 (x). General solution: yh (x) = c1 e x + 1 (xx , yp1 (x) = < 1. x) + M2 cos(2x). Form of particular solution: For F c2 e): 1 < x M1 sin(2 x RHSF2 (x): yp2 (x) = Le x . FThis=is already 2e solution(x) + F2 (x). = F1 of the associated homogeneous For of inhomogeneous DE: (x) sin(2x) a Form of particular solution: yp2(xF1=xLxep1x .x) = M1 sin(2x) + M2 cos(...
View Full Document

This document was uploaded on 02/09/2014.

Ask a homework question - tutors are online