y" + 100y = sec²(10z) (1) Let C1 and C2 be arbitrary constants. The general solution to the related homogeneous differential equation y" + 100y = 0 is the function y, (x) = C1 Y1(x) + C2 Y2(x) = Cı +C2 NO TE: The order in which you enter the answers is important; that is, Cif(x)+ C29(x) # C19(x) + C2f(r). (2) The particular solution yp(x) to the differential equation y" + 100y = sec²(10x) is of the form yp(z) = y1 (x) u, (z) + 2(x) u2(x) where u (z) = and u(x) = (3) It follows that u (2) and u2(x) = ; thus Yp(x) (4) The most general solution to the non-homogeneous differential equation y" + 100y = sec²(10x) is y = C, %3D +C2
y" + 100y = sec²(10z) (1) Let C1 and C2 be arbitrary constants. The general solution to the related homogeneous differential equation y" + 100y = 0 is the function y, (x) = C1 Y1(x) + C2 Y2(x) = Cı +C2 NO TE: The order in which you enter the answers is important; that is, Cif(x)+ C29(x) # C19(x) + C2f(r). (2) The particular solution yp(x) to the differential equation y" + 100y = sec²(10x) is of the form yp(z) = y1 (x) u, (z) + 2(x) u2(x) where u (z) = and u(x) = (3) It follows that u (2) and u2(x) = ; thus Yp(x) (4) The most general solution to the non-homogeneous differential equation y" + 100y = sec²(10x) is y = C, %3D +C2
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
Transcribed Image Text:y" + 100y = sec²(10x)
%3D
(1) Let C1 and C2 be arbitrary constants. The general solution to the related homogeneous
differential equation y" + 100y = 0 is the function y, (x) = C1 41(x)+ C2 Y2(x) = C1
+C2
NOTE: The order in which you enter the answers is important; that is,
Cif(x) + C29(x) + C19(x) + C2f(x).
(2) The particular solution yp(x) to the differential equation y" + 100y = sec²(10x) is of the
form yp(x) = Y1(x) u1(x) + Y½(x) U2(x) where u' (x) =
and
u, (z) =
%3D
(3) It follows that u1(x) :
and u2(x) =
; thus yp(x) =
(4) The most general solution to the non-homogeneous differential equation
y" + 100y = sec2²(10x) is
y = C1
+C2
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.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,
