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Differential Equation — Minor 2 2023 question paper

MMMUT Mechanical Engineering previous year question paper for Differential Equation (BSM-102), semester 1, Minor 2 2023. All 8 questions are listed below, each with a written answer on Nexsus.

Paper details

  • Subject: Differential Equation (BSM-102)
  • Branch: Mechanical Engineering
  • Semester: 1
  • Exam: Minor 2 2023
  • Questions: 8

Questions asked in Differential Equation Minor 2 2023

  1. Q1. Attempt any two parts of the following. Q1(a) is compulsory.
  2. Q1(a). Find the partial differential equation of (i) x^2 + y^2 + (z - a)^2 = b^2 (ii) z = f(x^2 - y^2) [5 marks]
  3. Q1(b). Solve x^2p^2 + y^2q^2 = z^2 [3 marks]
  4. Q1(c). Solve the Partial Differential Equation ∂^2z/∂x^2 - 3∂^2z/∂x∂y + 2∂^2z/∂y^2 = e^(2x - y) + e^(x + y) + cos(x + 2y) [3 marks]
  5. Q2. Attempt any two parts of the following. Q2(a) is compulsory.
  6. Q2(a). A string is stretched and fastened to two points f apart. Motion is started by displacing the string into the form y = k(lx - x^2) form which it is released at time t = 0. Find the displacement of any point on the string at a distance of x from one end at time t. [4 marks]
  7. Q2(b). Solve the equation ∂u/∂t = ∂^2u/∂x^2 with boundary condition u(x,0) = 3sin(nπx), u(0,t) = u(l,t) = 0 where 0 < x < l. [3 marks]
  8. Q2(c). Using the method of separation of variables, solve ∂u/∂x = 2∂u/∂t + u where u(x,0) = 6e^(-3x) [3 marks]