Consider the following Sturm-Liouville problem:(e"d')' + de®¢ = 0, 0

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Answered: Consider the following Sturm-Liouville…

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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Question 1 Identify the correct M and N for the following differential equations, then test for exactness: a) 2xyx+x'dy-0 c) x²y³dx+3x²y=0 b) 2xe dr+x'e'dy-0 c) (1-xy)+(2y-x'y)dy-0 (xsin 2y+e)dx+(x cos2y + x)dy=0 d) (x²-sin(3y))dx-3xcos(3y)dy-0 Question 2 Find a, fand er if all the following equations are EXACT. a) (x+y)dx+(2x+y)dy=0 b) (x+2y)dx+(x+y)dy-0 c) (+axy-2x)+(3y² + 20x'y")dy-0 Question 3 Find the solutions for the following differential equations. a) x'ydr- b) (2x-x)dx-xydy-0 c) (ye+e)de+(-3)dy-0 d) (3x + ycos(x))dx + (sin(x)-4y')-0 =0 Question 4 Find the particular solution: a) (2xy +6x) dx+(x+2y)dy-0 (0) 3 b) (²-2)dx+(xy+1)dy-0 (0)-4 c) (cos(3x)+2y) de+ (2x+sin(3x))=0 (0)-1
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Consider the following Sturm-Liouville problem: (e"d')' + de®¢ = 0, 0