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4. (a) Show that F (2xy + z³)i+x²j+3xz²k is conservative force field. Find the scalar potential of F. (b) Check the existence and uniqueness of the solution of the initial value problem (IVP) 3xy y = 2+ cos xy exists. ; y(0) = 0; R: x ≤ 1, y ≤ 2. Also specify interval in which the solutions

4. (a) Show that F (2xy + z³)i+x²j+3xz²k is conservative force field. Find the scalar potential of F. (b) Check the existence and uniqueness of the solution of the initial value problem (IVP) 3xy y = 2+ cos xy exists. ; y(0) = 0; R: x ≤ 1, y ≤ 2. Also specify interval in which the solutions

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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4. (a) Show that F = (2xy + z³)i+x²+3xz²k is conservative force field. Find the scalar potential of F. (b) Check the existence and uniqueness of the solution of the initial value problem (IVP) 3xy 1 y = exists. 2+ cos xy ; y(0) = 0; R: x ≤ 1, y ≤ 2. Also specify interval in which the solutions
Transcribed Image Text:4. (a) Show that F = (2xy + z³)i+x²+3xz²k is conservative force field. Find the scalar potential of F. (b) Check the existence and uniqueness of the solution of the initial value problem (IVP) 3xy 1 y = exists. 2+ cos xy ; y(0) = 0; R: x ≤ 1, y ≤ 2. Also specify interval in which the solutions
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