This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 1 2. Consider the equation u xx + u yy = 0 (with no boundary conditions). Use separation of variables to Fnd all solutions of the form u ( x, y ) = F ( x ) G ( y ). Be sure to consider each case for the constant k which arises in this method: a. (5) k = 0 b. (20) k = p 2 > 0. c. (5) k =p 2 < 0. 2 3. (25) A vibrating string of length (with c 2 = 1) is described in general by u ( x, t ) = X n =1 ( A n cos nt + B n sin nt )sin nx Find u ( x, t ) if the initial displacement (at t = 0) is 2sin xsin3 x and the initial velocity is sin3 x . 3 4. (15) Solve the hyperbolic equation u xx = u xy in the manner of DAlembert by substituting v = y and z = x + y . 4...
View
Full
Document
This note was uploaded on 01/06/2012 for the course MATH 4038 taught by Professor Staff during the Summer '08 term at LSU.
 Summer '08
 Staff

Click to edit the document details