(a) Here we have F = y² + w²y² + 2y (a sin wx+bsinh wx), so F₁ = 2y' and Fy = 2w²y + 2(a sin wx + b sinh wx), and by (4.2) in the course notes the Euler-Lagrange equation is Solve y" - w2y = a sin wx+bsinh wx, y(1) = 0, y(2) = 1. (b) Because of the boundary conditions, it is convenient to write the general solution of the homogeneous equation y" — w²y = 0 in the form - c = a sinh(c(2 − 1))+Bsinh(c(2 −2)), - where a and ẞ are constants. A particular solution of the inhomogeneous equation y" — w²y = a sin wx + b sinh wx is y = p cos wx + q sin wx + rx coshwx + sx sinhwx, and substituting this into the equation gives p = 0, q = −a/(2w²), r = b/(2w), s = 0. Hence the general solution is I how come?? - y = a sinh(@(2 − 1)) +ßsinh(c( −2)) - a sin wx 2w2 bx cosh wx + 2w
(a) Here we have F = y² + w²y² + 2y (a sin wx+bsinh wx), so F₁ = 2y' and Fy = 2w²y + 2(a sin wx + b sinh wx), and by (4.2) in the course notes the Euler-Lagrange equation is Solve y" - w2y = a sin wx+bsinh wx, y(1) = 0, y(2) = 1. (b) Because of the boundary conditions, it is convenient to write the general solution of the homogeneous equation y" — w²y = 0 in the form - c = a sinh(c(2 − 1))+Bsinh(c(2 −2)), - where a and ẞ are constants. A particular solution of the inhomogeneous equation y" — w²y = a sin wx + b sinh wx is y = p cos wx + q sin wx + rx coshwx + sx sinhwx, and substituting this into the equation gives p = 0, q = −a/(2w²), r = b/(2w), s = 0. Hence the general solution is I how come?? - y = a sinh(@(2 − 1)) +ßsinh(c( −2)) - a sin wx 2w2 bx cosh wx + 2w
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:(a) Here we have F = y² + w²y² + 2y (a sin wx+bsinh wx), so F₁ = 2y' and
Fy = 2w²y + 2(a sin wx + b sinh wx), and by (4.2) in the course notes the
Euler-Lagrange equation is
Solve
y" - w2y = a sin wx+bsinh wx,
y(1) = 0, y(2) = 1.
(b) Because of the boundary conditions, it is convenient to write the general
solution of the homogeneous equation y" — w²y = 0 in the form
-
c = a sinh(c(2 − 1))+Bsinh(c(2 −2)),
-
where a and ẞ are constants. A particular solution of the inhomogeneous
equation y" — w²y = a sin wx + b sinh wx is
y = p cos wx + q sin wx + rx coshwx + sx sinhwx, and substituting this into the
equation gives p = 0, q = −a/(2w²), r = b/(2w), s = 0. Hence the general
solution is
I how come??
-
y = a sinh(@(2 − 1)) +ßsinh(c( −2))
-
a sin wx
2w2
bx cosh wx
+
2w
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 2 steps
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,
