Ordinary and Partial Differential Equation

Daffodil International University Department of Electrical and Electronic Engineering Faculty of Engineering Midterm Examination, Fall-2026 Course Code: 0541-121 Course Title: Ordinary and Partial Differential Equation Section: A, B, C, D, E, F Level-Term: L1-T2 Teacher's Initial: IJM,SS Full Marks: 25 Exam Date: Oct 31, 2026 Time: 1.5 Hours [Answer all the following questions] [The second right-most column indicates the COs with the respective Bloom's level] [The right-most column indicates the assigned marks] Q1. (a) Explain Homogeneous differential equation. CO-1 (C2) [1] (b) Identify the order, degree, and linearity or nonlinearity of the following differential equation with justification: [3] i. d^3y/dx^3 = ((dy/dx)^2)^(1/5) + 5(dy/dx) + y ii. y''' . y''' + sin y = x^5 y (c) Express y = e^x (A cos x + B sin x) in the form of an ODE. [2] Q2. Solve the following differential equations: CO-2 (C3) [3 × 4 = 12] i. dy/dx = y/x + cos(y/x) ii. dy/dx = (6x - 10y + 3)/(3x - 5y + 5) iii. cos x dy + (y sin x - 1) dx = 0; y(0) = 1 Q3. (a) The variation of resistance, R ohms, of an aluminium conductor with temperature °C is given by dR/dθ = αR, where α is the temperature coefficient of resistance of aluminium. If R = R0 when θ = 0°C, compute the equation for R. CO-2 (C3) [3] (b) An RC circuit has an emf of 300cos2t V, a resistance of 150 Ω, a capacitance of 1/6 × 10^-2 F, and an initial charge on the capacitor of 5 C. Determine [4] i. the charge on the capacitor at any time t ii. the steady-state current and iii. the transient current.