Consider the initial value problem dy dx 2 COS X + y sin x = 4x cos x and y (a) The general solution of the differential equation is: О А. OB. O C. y(x) 2 y(x) = x² O D. None of the answers given is correct OE. 2 = x (C + cos x), C arbitrary constant y(x) = (2x² + c) cos x, C arbitrary constant O E. (b) The solution of the initial value problem is O A. y(x) = (2x² - 3m²) OB. None of the answers given is correct = x (C + sin x), C arbitrary constant y(x) = (2x² +c) sin x, C arbitrary constant OC. y(x) = (2x² - 3R²) sin x O D. 471/2) y(x) 2. y(x) =X 2N = = X COS X COS X sin x - 47√2) - 23 x² √2 16 Hint: Up to an additive constant and for 0 < x < A NE we have
Consider the initial value problem dy dx 2 COS X + y sin x = 4x cos x and y (a) The general solution of the differential equation is: О А. OB. O C. y(x) 2 y(x) = x² O D. None of the answers given is correct OE. 2 = x (C + cos x), C arbitrary constant y(x) = (2x² + c) cos x, C arbitrary constant O E. (b) The solution of the initial value problem is O A. y(x) = (2x² - 3m²) OB. None of the answers given is correct = x (C + sin x), C arbitrary constant y(x) = (2x² +c) sin x, C arbitrary constant OC. y(x) = (2x² - 3R²) sin x O D. 471/2) y(x) 2. y(x) =X 2N = = X COS X COS X sin x - 47√2) - 23 x² √2 16 Hint: Up to an additive constant and for 0 < x < A NE we have
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:Consider the initial value problem
dy
dx
(7)
4
(a) The general solution of the differential equation is:
OA.
COS X
O B.
O C.
O D.
2
sin x = 4x cos x and
2
y(x)
OE.
= x (C + cos x), C arbitrary constant
y(x) = (2x² + c) cos x, C arbitrary constant
O C.
2
y(x)
= x (C+ sin x), C arbitrary constant
OD. None of the answers given is correct
O E.
y(x) = (2x² + c) sin x, C arbitrary constant
(b) The solution of the initial value problem is
O A.
y(x) = (2x² - 3²)
OB. None of the answers given is correct
y(x) = (2x²-3x²)
y(x)
= X
2
y(x) = x²
1
COS X -
sin X-
cos X
y
sin x
47√√2
2
471/2)
=
23 x² √2
16
Hint: Up to an additive constant and for 0 < x <
E|N
we have
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