Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Consider the following boundary value problem (E) : h + u = t2, r > 0, t>0 (1) (2) (3) u(r, 0) - cha, r>0 u(0, t) – 0, t>0 and suppose that ach(r) – sh(x) I = [*ch(2}dz = «ch{z) - sh(2), a +c. - 1 (1) By applying the Laplace transform to equation (1) of (E) (acting to the variable t) and by using equation (2) of (E), we obtain the following ODE: 3 a. Uz(r, s) + sU(r, s) = -cha – 2 b. U-(r, s) + sU(r, s) = -cha +- 2 c. Uz(r, s) + sU(r, s) = chx + d. None of the above (2) Using equation (3) of (E), the solution of the ODE obtained in part (2) is: shz s2 - 1 2 2 a. U(r, s) = chr- s2 - 1 s4 chr b. U(r, s) = shr 1 82 1 shr chr c. U(r,s) + 1 d. None of the above (3) The general solution of (E) is: (H(t – a) is the unit step function) a. u(z, t) = t³ + (t – x)®H(t – x) + cos(t – æ)H(t – x) b. u(r, t) = cha cost – shr sint + (t – r)*H(t – r) c. u(r, t) = cha cost – shr sint + t -(t- 2)*H(t – r) – cos(t – 2)H(t – r) d. None of the above

Consider the following boundary value problem (E) : h + u = t2, r > 0, t>0 (1) (2) (3) u(r, 0) - cha, r>0 u(0, t) – 0, t>0 and suppose that ach(r) – sh(x) I = [*ch(2}dz = «ch{z) - sh(2), a +c. - 1 (1) By applying the Laplace transform to equation (1) of (E) (acting to the variable t) and by using equation (2) of (E), we obtain the following ODE: 3 a. Uz(r, s) + sU(r, s) = -cha – 2 b. U-(r, s) + sU(r, s) = -cha +- 2 c. Uz(r, s) + sU(r, s) = chx + d. None of the above (2) Using equation (3) of (E), the solution of the ODE obtained in part (2) is: shz s2 - 1 2 2 a. U(r, s) = chr- s2 - 1 s4 chr b. U(r, s) = shr 1 82 1 shr chr c. U(r,s) + 1 d. None of the above (3) The general solution of (E) is: (H(t – a) is the unit step function) a. u(z, t) = t³ + (t – x)®H(t – x) + cos(t – æ)H(t – x) b. u(r, t) = cha cost – shr sint + (t – r)*H(t – r) c. u(r, t) = cha cost – shr sint + t -(t- 2)*H(t – r) – cos(t – 2)H(t – r) d. None of the above

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
laplace part 3
Consider the following boundary value problem (E) : h + u = t2, r > 0, t>0 (1) (2) (3) u(r, 0) - cha, r>0 u(0, t) – 0, t>0 and suppose that ach(r) – sh(x) I = [*ch(2}dz = «ch{z) - sh(2), a +c. - 1 (1) By applying the Laplace transform to equation (1) of (E) (acting to the variable t) and by using equation (2) of (E), we obtain the following ODE: 3 a. Uz(r, s) + sU(r, s) = -cha – 2 b. U-(r, s) + sU(r, s) = -cha +- 2 c. Uz(r, s) + sU(r, s) = chx + d. None of the above (2) Using equation (3) of (E), the solution of the ODE obtained in part (2) is: shz s2 - 1 2 2 a. U(r, s) = chr- s2 - 1 s4 chr b. U(r, s) = shr 1 82 1 shr chr c. U(r,s) + 1 d. None of the above (3) The general solution of (E) is: (H(t – a) is the unit step function) a. u(z, t) = t³ + (t – x)®H(t – x) + cos(t – æ)H(t – x) b. u(r, t) = cha cost – shr sint + (t – r)*H(t – r) c. u(r, t) = cha cost – shr sint + t -(t- 2)*H(t – r) – cos(t – 2)H(t – r) d. None of the above
Transcribed Image Text:Consider the following boundary value problem (E) : h + u = t2, r > 0, t>0 (1) (2) (3) u(r, 0) - cha, r>0 u(0, t) – 0, t>0 and suppose that ach(r) – sh(x) I = [*ch(2}dz = «ch{z) - sh(2), a +c. - 1 (1) By applying the Laplace transform to equation (1) of (E) (acting to the variable t) and by using equation (2) of (E), we obtain the following ODE: 3 a. Uz(r, s) + sU(r, s) = -cha – 2 b. U-(r, s) + sU(r, s) = -cha +- 2 c. Uz(r, s) + sU(r, s) = chx + d. None of the above (2) Using equation (3) of (E), the solution of the ODE obtained in part (2) is: shz s2 - 1 2 2 a. U(r, s) = chr- s2 - 1 s4 chr b. U(r, s) = shr 1 82 1 shr chr c. U(r,s) + 1 d. None of the above (3) The general solution of (E) is: (H(t – a) is the unit step function) a. u(z, t) = t³ + (t – x)®H(t – x) + cos(t – æ)H(t – x) b. u(r, t) = cha cost – shr sint + (t – r)*H(t – r) c. u(r, t) = cha cost – shr sint + t -(t- 2)*H(t – r) – cos(t – 2)H(t – r) d. None of the above
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
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,
SEE MORE TEXTBOOKS