Mathematics-II exam (MS 103) from BUTEX affiliated colleges' 2023 Level-1 Term-II finals. Covers homogeneous and exact differential equations, conservative and solenoidal vectors, div-curl identities, analytic functions, and Laplace transform applications.
Level-1 Term-II, Final Exám-2023
Subject: Mathematics-II (Code: MS 103)
Time: 3.0 Hrs. Full Marks: 72
(Use separate answer script for Part: A and Part: B)
(All parts of a question must be answered consecutively)
Part: A
(Answer any three questions)
1. (a) Define homogeneous differential equation. Solve the equation by this method.
(b) Write down the rules for finding the solution of an exact equation.
(c) Solve
[4+4+4=12]
2. (a) Solve:
(b) Solve:
(c) Solve:
[4+4+4=12]
3. (a) If are three vectors then prove that
(b) Determine constant a and b such that vector is conservative.
(c) Find the value of n for which the vector is solenaidal.
[4+4+4=12]