Find the particular solutions satisfying the given conditions: dy a) y = 2 when x = 0. dx = 1 + cos x + cos²x,
Find the particular solutions satisfying the given conditions: dy a) y = 2 when x = 0. dx = 1 + cos x + cos²x,
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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Transcribed Image Text:2.2 Find the particular solutions satisfying the given conditions:
dy
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
a)
dx
2
= 1 + cos x + cos²x,
y = 2 when x =
0.
Transcribed Image Text:-2
dy
b) = 1 - 2x - 3x-²,
dx
c) e²x dy
-
dx
d) = (x +
að al
e)
dy
dx
+ 1 = 0,
dx
18
f) x²x² dy
dx
2
dy = x√√₁ + x²₂
2
= x³,
y = -1 when x = 1.
y → 2 as x→∞.
y = 1 when x =
1.
y = -3 when x = (
0.
y(0) = 1.
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