About this previous year paper
This question paper covers advanced topics of Differential Equations, Partial Differential Equations, Laplace Transforms, Fourier Series, Bessel Functions, and Legendre Polynomials.
It is divided into three sections testing conceptual understanding, analytical problem-solving, and application of mathematical methods.
SECTION – A (10 × 2 = 20 Marks)
This section contains ten short questions, each testing a fundamental concept or formula.
Topics include:
Showing a differential equation represents parabolas
Classification of PDEs
Particular integral of differential equations
Dirichlet’s conditions for Fourier series
Bessel function identity
Laplace transform shifting property
Laplace transform of sin(at)/t
One- and two-dimensional wave equations
Fourier constant term
Generating function of Legendre polynomials
This section focuses on definitions, proofs, identities, and small computations.
SECTION – B (5 × 10 = 50 Marks)
Students must attempt any five medium-length questions involving derivations and problem-solving.
Topics include:
Solving linear differential equations with operator method
Recurrence relation for Legendre polynomials
Series solution of differential equations
Solving ODEs using Laplace transforms with given initial conditions
Fourier series expansion of piecewise functions and deduced results
Solving Laplace equations with boundary conditions
Solving PDE using operator notation
Inverse Laplace transform using convolution theorem
This section tests higher-level computation, series methods, PDE solving, and transform techniques.
SECTION – C (2 × 15 = 30 Marks)
Students must attempt any two long descriptive questions.
Topics include:
Differential equations
Solving (D² – 2D + 1)y = eˣ sin x
Laplace method for integro-differential equations
Solving first-order PDE using Charpit’s method
Laplace transforms & Legendre polynomials
Laplace transform of (cos at – cos bt)/t
Expressing polynomials in Legendre form
Cosine series expansion for given interval
Bessel functions & wave equations
Identity for J₃(x) in terms of J₁(x) and J₀(x)
Solving first-order linear PDE
Displacement of a vibrating string with fixed ends and initial shape
This section evaluates analytical depth, derivation skills, and application of classical mathematical methods.