Consider the initial value problem (2xy² + cos x cosy) dx + (2x2y- sinx siny) dy = 0 and y(0) = 1 (a) Check whether the differential equation is OA. Separable B. Not exact OC. Exact because (2xy². + cos x cos OD. Exact because (2xy² 2xy 3 + OB. O C. 3 2x y 3 (b) The general solution of the differential equation is given by A. None of the given answers is correct B. 22 x y + sin x sin y - cos x cos y = C with C an arbirary constant C. 4xy + sin x sin y = C with C an arbirary constant D. 3 osy), = (2x²y- si osy) x + cos x cos 3y 22 x y + sin x cos y = 0 3 2xy + 2x 3 - sinx siny)x (2x²y- sin x siny), E E. 22 x²y² + sinx cos y = C with C an arbirary constant (c) The solution of the initial value problem is given implicitly by 22 xy + sinx siny- cos x cos y = + sin x sin y cos x cos y = C with C an arbirary constant - cos 1 + sin x sin y - cos x cos y = - cos 1
Consider the initial value problem (2xy² + cos x cosy) dx + (2x2y- sinx siny) dy = 0 and y(0) = 1 (a) Check whether the differential equation is OA. Separable B. Not exact OC. Exact because (2xy². + cos x cos OD. Exact because (2xy² 2xy 3 + OB. O C. 3 2x y 3 (b) The general solution of the differential equation is given by A. None of the given answers is correct B. 22 x y + sin x sin y - cos x cos y = C with C an arbirary constant C. 4xy + sin x sin y = C with C an arbirary constant D. 3 osy), = (2x²y- si osy) x + cos x cos 3y 22 x y + sin x cos y = 0 3 2xy + 2x 3 - sinx siny)x (2x²y- sin x siny), E E. 22 x²y² + sinx cos y = C with C an arbirary constant (c) The solution of the initial value problem is given implicitly by 22 xy + sinx siny- cos x cos y = + sin x sin y cos x cos y = C with C an arbirary constant - cos 1 + sin x sin y - cos x cos y = - cos 1
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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Question
part A
Transcribed Image Text:Consider the initial value problem
(2xy² + cos x cosy) dx + (2x²y- sinx siny) dy = 0 and y(0) = 1
cos
(a) Check whether the differential equation is
OA. Separable
B. Not exact
C.
Exact because (2xy² + cos x cos
cosy), = (2x²y- sinx sin y) x
C.
O D.
OD. Exact because (2xy² + cos x cos y
cos y) = (2x²y- sinx siny) y
(b) The general solution of the differential equation is given by
OA. None of the given answers is correct
OB.
B. x²y² + sinx siny - cos x cos y = C with C an arbirary constant
4xy+sin x sin y = C with C an arbirary constant
2xy 2x y
3
+ sin x sin y - cos x cos y = C with C an arbirary constant
OE. x²y² + sinx cos y = C with C an arbirary constant
2.2
(c) The solution of the initial value problem is given implicitly by
OA.
xy + sinx siny- cos x cos y = - cos 1
OB.
xy + sin x cos y = 0
O C. 3 3y
2xy + 2x
3
+ sin x siny − cos x cos y = - cos 1
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