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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe0184384-ba44-4564-8d57-1206acfb916e%2Fd494515a-df68-4517-b0eb-b1c13b010dea%2F51qksfd.png&w=3840&q=75)
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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