a) Use the method of Lagrange to find the general solution to XZx+2xzZy = 2. In the following cases determine whether a solution exists, and if so give it's most general form. (i) z = 2x on y = 2x on y = 2x² + 1. (ii) 2= 2x² on y = 3x³. (iii) z = x² on y = x³ – 1.
a) Use the method of Lagrange to find the general solution to XZx+2xzZy = 2. In the following cases determine whether a solution exists, and if so give it's most general form. (i) z = 2x on y = 2x on y = 2x² + 1. (ii) 2= 2x² on y = 3x³. (iii) z = x² on y = x³ – 1.
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:3. (a)
(b)
Use the method of Lagrange to find the general solution to
xZx + 2xzzy = 2.
In the following cases determine whether a solution exists, and if so give it's most
general form.
(i) z = 2x on y = 2x² + 1.
(ii) z = 2x² on y = 3x³.
(iii) z = x² on y = x³ – 1.
(i) The ends of a finite string of length are fixed. The initial displace-
ment is given by the function (x) = 2 sin(4x), the initial velocity is zero. Find
the vibrations of the string for t > 0,0 ≤ x ≤ π, that is, solve
= a²uxx,
u(t,0) = u(t, π) = 0,
u(0, x) = 2 sin(4x), ut(0, x) = 0.
Utta²
(ii) Now assume the string is infinite with the same initial conditions. Solve the
problem using d'Alembert's formula.
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 5 steps with 4 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,
