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We are given a differential equation and will rewrite it in the form M(x, y) dx + N(x, y) dy = 0. xy² dy y³ – x³ dx = xy² dy xy² dy (y³x³) dx = 0 xy² dy + (-y³ + x³) dx = 0 Find the functions M and N. = (y³ – x³) dx M(x, y) = x³ln(x) + 4 (1³ 3 3 – x³) = 0 - 3 N(x, y) = x³ln(x) + 4(1,³ x ³) = 0 - X X

We are given a differential equation and will rewrite it in the form M(x, y) dx + N(x, y) dy = 0. xy² dy y³ – x³ dx = xy² dy xy² dy (y³x³) dx = 0 xy² dy + (-y³ + x³) dx = 0 Find the functions M and N. = (y³ – x³) dx M(x, y) = x³ln(x) + 4 (1³ 3 3 – x³) = 0 - 3 N(x, y) = x³ln(x) + 4(1,³ x ³) = 0 - X X

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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We are given a differential equation and will rewrite it in the form M(x, y) dx + N(x, y) dy = 0. xy² dy y³ – x³ dx = xy² dy xy² dy (y³x³) dx = 0 xy² dy + (-y³ + x³) dx = 0 Find the functions M and N. = (y³ – x³) dx 3 3 M(x, y) = x³ln(x) + 4 (1³ – x³) = 0 - N(x, y) = x³ln(x) + 4(y³ – x³) = 0 X X
Transcribed Image Text:We are given a differential equation and will rewrite it in the form M(x, y) dx + N(x, y) dy = 0. xy² dy y³ – x³ dx = xy² dy xy² dy (y³x³) dx = 0 xy² dy + (-y³ + x³) dx = 0 Find the functions M and N. = (y³ – x³) dx 3 3 M(x, y) = x³ln(x) + 4 (1³ – x³) = 0 - N(x, y) = x³ln(x) + 4(y³ – x³) = 0 X X
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