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Substitute c4 = -c3y in the equation (6), Y() = 0 (7) Substitute the value of X (x) from equation (5) and the value of Y (v) from equation (7) in equation (1), u (x, y) = 0 When à = -a', substitute à = -a² in equation (2), X" - a'X = 0 The general solution of the above equation is, X (x) = c1 cosh ax + c2 sinh ax (8) At boundary conditions u (0, y) = 0 and u (a, y) = 0, so the value of c; is 0 also written as e = 0, Substitute e = 0 in the equation (8), X (x) = c2 sinh ax (9) Substitute à = -a² in equation (3), y" + a²Y = 0 The general solution of the above equation is, Y (9) = c3 cos ay + c4 sin ay (10) At boundary conditions u (0, y) = 0, u (a, y) = 0 and = 0,

Substitute c4 = -c3y in the equation (6), Y() = 0 (7) Substitute the value of X (x) from equation (5) and the value of Y (v) from equation (7) in equation (1), u (x, y) = 0 When à = -a', substitute à = -a² in equation (2), X" - a'X = 0 The general solution of the above equation is, X (x) = c1 cosh ax + c2 sinh ax (8) At boundary conditions u (0, y) = 0 and u (a, y) = 0, so the value of c; is 0 also written as e = 0, Substitute e = 0 in the equation (8), X (x) = c2 sinh ax (9) Substitute à = -a² in equation (3), y" + a²Y = 0 The general solution of the above equation is, Y (9) = c3 cos ay + c4 sin ay (10) At boundary conditions u (0, y) = 0, u (a, y) = 0 and = 0,

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I don't understand why X(x)=c1cosh(ax)+c2sinh(ax) and Y(y)=c3cos(ay)+c4sin(ay). Can you please explain it to me? Thank you

Safari File Edit View History Bookmarks Window Help Sun 10:03 PM bartleby.com Bing In Problems 1-10 solve Laplace's equation (1) for a rectangular plate subject to the given boundary. Yahoo + = bartleby Screen Shot 2021-03...8.58 PM Q Search for textbooks, step-by-step explanations to homework questions.. Ask an Expert E Bundle: Differential Equations with Bou... < Chapter 12.5, Problem 2E > Screen Shot 2021-03...9.01 PM Substitute c4 = -c3y in the equation (6), Y (y) = 0 (7) Substitute the value of X (x) from equation (5) and the value of Y (y) from equation (7) in equation (1), и (х, у) 3D 0 When A = -a² , substitute à = -a² in equation (2), X" – a²X = 0 The general solution of the above equation is, X (x) = c1 cosh ax + c2 sinh ax (8) At boundary conditions u (0, y) = 0 and u (a, y) = 0, so the value of c1 is 0 also written as ci = 0. Substitute c1 = 0 in the equation (8), X (x) = c2 sinh ax (9) Substitute 1 = -a² in equation (3), Y" + a?Y = 0 The general solution of the above equation is, X GET 10 FREE QUESTIONS Y (y) = c3 cos ay + c4 sin ay (10) Privacy - Terms At boundary conditions u (0, y) = 0, u (a, y) = 0 and = 0, MAR 14 étv ARCHIVE
Transcribed Image Text:Safari File Edit View History Bookmarks Window Help Sun 10:03 PM bartleby.com Bing In Problems 1-10 solve Laplace's equation (1) for a rectangular plate subject to the given boundary. Yahoo + = bartleby Screen Shot 2021-03...8.58 PM Q Search for textbooks, step-by-step explanations to homework questions.. Ask an Expert E Bundle: Differential Equations with Bou... < Chapter 12.5, Problem 2E > Screen Shot 2021-03...9.01 PM Substitute c4 = -c3y in the equation (6), Y (y) = 0 (7) Substitute the value of X (x) from equation (5) and the value of Y (y) from equation (7) in equation (1), и (х, у) 3D 0 When A = -a² , substitute à = -a² in equation (2), X" – a²X = 0 The general solution of the above equation is, X (x) = c1 cosh ax + c2 sinh ax (8) At boundary conditions u (0, y) = 0 and u (a, y) = 0, so the value of c1 is 0 also written as ci = 0. Substitute c1 = 0 in the equation (8), X (x) = c2 sinh ax (9) Substitute 1 = -a² in equation (3), Y" + a?Y = 0 The general solution of the above equation is, X GET 10 FREE QUESTIONS Y (y) = c3 cos ay + c4 sin ay (10) Privacy - Terms At boundary conditions u (0, y) = 0, u (a, y) = 0 and = 0, MAR 14 étv ARCHIVE
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