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Ordinary and Partial Differential Equations — Minor 2 2021 question paper

MMMUT Electrical Engineering previous year question paper for Ordinary and Partial Differential Equations (BSM-102), semester 1, Minor 2 2021. All 11 questions are listed below, each with a written answer on Nexsus.

Paper details

  • Subject: Ordinary and Partial Differential Equations (BSM-102)
  • Branch: Electrical Engineering
  • Semester: 1
  • Exam: Minor 2 2021
  • Questions: 11

Questions asked in Ordinary and Partial Differential Equations Minor 2 2021

  1. Q1(a)(i). Solve the PDE x^2(y - z)p + y^2(z - x)q = z^2(x - y). [6 marks]
  2. Q1(a)(ii). Solve the PDE: r + s - 6t = y sinx. [6 marks]
  3. Q1(b). Use Charpit's method to find the complete integral of following P.D.E: z^2 = pqxy. [4 marks]
  4. Q1(c)(i). Eliminate the arbitrary function f from z = f(xy/z) and form the partial differential equation. [4 marks]
  5. Q1(c)(ii). Define Integral surface of the PDE and obtain the singular integral of the PDE z = px + qy + sqrt(p^2 + q^2) [4 marks]
  6. Q2(a)(i). Solve the following P.D.E. by the method of separation of variable: u_x = 2u_t + u with u(x, 0) = 6e^-3x. [6 marks]
  7. Q2(a)(ii). A tightly starched string with fixed end points x = 0 and x = l is initially in a position given by y = a sin (pi x / l). If it is released from rest from its position, find the displacement y(x, t). [6 marks]
  8. Q2(b). Solve ∂²u/∂x² + ∂²u/∂y² = 0 which satisfies the condition u(0, y) = u(l, y) = u(x, 0) = 0 and u(x, a) = sin (pi x / l). [4 marks]
  9. Q2(c). An initially long uniform plate is bounded by two parallel edges and an end at right angle to them. The breadth is pi, the end is maintained at a temperare 100° c at all points and other edges are at 0°C. Find the state temperature. [4 marks]
  10. QQ.1. Attempt any Two parts of the following. Q. 1 (a) is compulsory.
  11. QQ.2. Attempt any Two parts of the following. Q. 2 (a) is compulsory.