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J (sin 3x)² = sin 3x xp- sin 3x CO = sin 3x xp- sin 3x On simplifying further, y2 (x) = cq sin 3x / cos ec?3xdx = -Co sin 3x= cot 3x 3 - sin 3x cos 3x sin 3x - cos 3x Therefore, y2 (x) = -cos 3x = C cos 3x [C = - II y2 (x) = cos 3x Hence, the second solution of the differential equation is у2 (х) %3D сos 3x.

J (sin 3x)² = sin 3x xp- sin 3x CO = sin 3x xp- sin 3x On simplifying further, y2 (x) = cq sin 3x / cos ec?3xdx = -Co sin 3x= cot 3x 3 - sin 3x cos 3x sin 3x - cos 3x Therefore, y2 (x) = -cos 3x = C cos 3x [C = - II y2 (x) = cos 3x Hence, the second solution of the differential equation is у2 (х) %3D сos 3x.

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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What happens to the arbitrary constant C? Why isn't it included in the final answer?

J (sin 3x)² = sin 3x xp- sin 3x CO = sin 3x xp- sin 3x On simplifying further, y2 (x) = cq sin 3x / cos ec?3xdx = -Co sin 3x= cot 3x 3 - sin 3x cos 3x sin 3x - cos 3x Therefore, y2 (x) = -cos 3x = C cos 3x [C = - II y2 (x) = cos 3x Hence, the second solution of the differential equation is у2 (х) %3D сos 3x.
Transcribed Image Text:J (sin 3x)² = sin 3x xp- sin 3x CO = sin 3x xp- sin 3x On simplifying further, y2 (x) = cq sin 3x / cos ec?3xdx = -Co sin 3x= cot 3x 3 - sin 3x cos 3x sin 3x - cos 3x Therefore, y2 (x) = -cos 3x = C cos 3x [C = - II y2 (x) = cos 3x Hence, the second solution of the differential equation is у2 (х) %3D сos 3x.
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