Find the general solution of the differential equation: (1 + cos(x))y' - (sin(x))y = 2x + (-1 + con(a). sin(x) 2x Step zero, the standard form of the equation is: y' + = 1+ cos(x) First real step, determine the integrating factor Integrating factor = Second, multiply both sides by the integrating factor. Third, rewrite the equation in the form [f(x, y)]' = g(x) f(x, y) = g(x) = Lastly, integrate to determine the general solution to the equation, using c for your constant of integration: y =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
@
2
Find the general solution of the differential equation: (1 + cos(x))y' - (sin(x))y = 2x
sin(x)
Step zero, the standard form of the equation is: y' +
+(₁
y =
2x
1 + cos(x)
1 + cos(x)
First real step, determine the integrating factor
Integrating factor =
Second, multiply both sides by the integrating factor.
Third, rewrite the equation in the form [f(x, y)]' = g(x)
f(x, y) =
g(x) =
Lastly, integrate to determine the general solution to the equation, using c for your constant of
integration:
y =
C
2
W
S
X
# 3
e
d
с
C
54
$
r
f
otos
%
5
V
rt
g
Oll
6
b
y
&
7
h
O
u
n
8
j
(
9
m
k
✓
)
0
Transcribed Image Text:@ 2 Find the general solution of the differential equation: (1 + cos(x))y' - (sin(x))y = 2x sin(x) Step zero, the standard form of the equation is: y' + +(₁ y = 2x 1 + cos(x) 1 + cos(x) First real step, determine the integrating factor Integrating factor = Second, multiply both sides by the integrating factor. Third, rewrite the equation in the form [f(x, y)]' = g(x) f(x, y) = g(x) = Lastly, integrate to determine the general solution to the equation, using c for your constant of integration: y = C 2 W S X # 3 e d с C 54 $ r f otos % 5 V rt g Oll 6 b y & 7 h O u n 8 j ( 9 m k ✓ ) 0
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,