Give the general solution of the differential equation p"+ 25 y =2 sec( 5 x) a) O y=C, sin(5 x) + C, cos( 5 x) + x cos( 5 x) + 25 cos( 5 x) In (cos(5 x)|) 2 b) O y=C, sin(5x) + C, cos( 5 x) +x sin (5 x) + sin (5 x) In(cos(5 x)|) 2 x sin (5 x) + 2 c) O y=C, sin(5 x) + C, cos( 5 x) + cos( 5 x) In(lcos( 5 x)|) 25 d) O y=C, e"+C,e° 5*+ sin(5 x) + 2 cos( 5 x) In (cos(5x)) -5x 25 e) O y-C, e* + C, e*+ sin( 5 x) + 2 sin (5x) In (cos(5 x)|) 25 f) None of the above.
Give the general solution of the differential equation p"+ 25 y =2 sec( 5 x) a) O y=C, sin(5 x) + C, cos( 5 x) + x cos( 5 x) + 25 cos( 5 x) In (cos(5 x)|) 2 b) O y=C, sin(5x) + C, cos( 5 x) +x sin (5 x) + sin (5 x) In(cos(5 x)|) 2 x sin (5 x) + 2 c) O y=C, sin(5 x) + C, cos( 5 x) + cos( 5 x) In(lcos( 5 x)|) 25 d) O y=C, e"+C,e° 5*+ sin(5 x) + 2 cos( 5 x) In (cos(5x)) -5x 25 e) O y-C, e* + C, e*+ sin( 5 x) + 2 sin (5x) In (cos(5 x)|) 25 f) None of the above.
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
will rate if correct!
![**Question 1**
Give the general solution of the differential equation
\[ y'' + 25y = 2 \sec(5x) \]
a) \( y = C_1 \sin(5x) + C_2 \cos(5x) + \frac{2}{5} x \cos(5x) + \frac{2}{25} \cos(5x) \ln(|\cos(5x)|) \)
b) \( y = C_1 \sin(5x) + C_2 \cos(5x) + \frac{2}{5} x \sin(5x) + \frac{2}{25} \sin(5x) \ln(|\cos(5x)|) \)
c) \( y = C_1 \sin(5x) + C_2 \cos(5x) + \frac{2}{5} x \sin(5x) + \frac{2}{25} \cos(5x) \ln(|\cos(5x)|) \)
d) \( y = C_1 e^{5x} + C_2 e^{-5x} + \frac{2}{5} \sin(5x) + \frac{2}{25} \cos(5x) \ln(|\cos(5x)|) \)
e) \( y = C_1 e^{5x} + C_2 e^{-5x} + \frac{2}{5} \sin(5x) + \frac{2}{25} \sin(5x) \ln(|\cos(5x)|) \)
f) \( \text{None of the above.} \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F88afae02-80d5-49da-ad82-a7933e6f4445%2F5c9b5d1c-25f0-4bc2-b901-ff60ba639a8b%2Fq15t8l_processed.png&w=3840&q=75)
Transcribed Image Text:**Question 1**
Give the general solution of the differential equation
\[ y'' + 25y = 2 \sec(5x) \]
a) \( y = C_1 \sin(5x) + C_2 \cos(5x) + \frac{2}{5} x \cos(5x) + \frac{2}{25} \cos(5x) \ln(|\cos(5x)|) \)
b) \( y = C_1 \sin(5x) + C_2 \cos(5x) + \frac{2}{5} x \sin(5x) + \frac{2}{25} \sin(5x) \ln(|\cos(5x)|) \)
c) \( y = C_1 \sin(5x) + C_2 \cos(5x) + \frac{2}{5} x \sin(5x) + \frac{2}{25} \cos(5x) \ln(|\cos(5x)|) \)
d) \( y = C_1 e^{5x} + C_2 e^{-5x} + \frac{2}{5} \sin(5x) + \frac{2}{25} \cos(5x) \ln(|\cos(5x)|) \)
e) \( y = C_1 e^{5x} + C_2 e^{-5x} + \frac{2}{5} \sin(5x) + \frac{2}{25} \sin(5x) \ln(|\cos(5x)|) \)
f) \( \text{None of the above.} \)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 3 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
