Consider the following boundary value problem (E) : *+ - t2, r>0, t>0 (1) u(r, 0) - cha, r>0 u(0, t) – 0, (2) (3) t>0 and suppose that ach(x) – sh(x) , a² – 1 (1) By applying the Laplace transform to equation (1) of (E) (acting to the variable t) and by - / c" ch(z)dz I = ear az + c. %3D using equation (2) of (E), we obtain the following ODE: 3 a. Uz(r, 8) + sU(r, s) = -chx %3D b. Uz(r, s) + sU(x, s) = -chr + 2 c. Uz(r, s) + sU(x, s) = chx + d. None of the above (2) Using equation (3) of (E), the solution of the ODE obtained in part (2) is: shr 2 2 a. U(r, s) = chxr- s2 -1 52 – 1 chr shr b. U(x, s) 1 shr s2 - 1 chr c. U(x, s) s2 -1 d. None of the above (3) The general solution of (E) is: (H(t – a) is the unit step function) a. u(r, t) = +(t – x)*H(t – x) + cos(t – x)H(t – x) %3D 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) : *+ - t2, r>0, t>0 (1) u(r, 0) - cha, r>0 u(0, t) – 0, (2) (3) t>0 and suppose that ach(x) – sh(x) , a² – 1 (1) By applying the Laplace transform to equation (1) of (E) (acting to the variable t) and by - / c" ch(z)dz I = ear az + c. %3D using equation (2) of (E), we obtain the following ODE: 3 a. Uz(r, 8) + sU(r, s) = -chx %3D b. Uz(r, s) + sU(x, s) = -chr + 2 c. Uz(r, s) + sU(x, s) = chx + d. None of the above (2) Using equation (3) of (E), the solution of the ODE obtained in part (2) is: shr 2 2 a. U(r, s) = chxr- s2 -1 52 – 1 chr shr b. U(x, s) 1 shr s2 - 1 chr c. U(x, s) s2 -1 d. None of the above (3) The general solution of (E) is: (H(t – a) is the unit step function) a. u(r, t) = +(t – x)*H(t – x) + cos(t – x)H(t – x) %3D 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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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