Engineering Mathematics-II Unit 1 – Ordinary Differential Equation of Higher Order: AKTU previous year questions
34 AKTU questions from Unit 1 (Ordinary Differential Equation of Higher Order) asked in 2019–2025, tagged by marks, year and topic. In short: about 42 marks of every paper come from this unit; the most asked topic is Linear ODE Constant Coefficients (14 times); 20 questions came back in a later year. The latest ones are listed below; on the page you can filter them by 2-mark or long questions, topic and repeats.
Unit 1 previous year questions
- Find the general solution of the following differential equation: d³y/dx³ + dy/dx = 0 (2 marks, 2025, Linear ODE Constant Coefficients)
- Find the Particular Integral for the following differential equation: y'' − 8y' + 16y = e^(4x) (2 marks, 2025, Linear ODE Constant Coefficients)
- Find the general solution of the differential equation y'' − 2y' + 2y = x + e^x cos x (7 marks, 2025, Linear ODE Constant Coefficients)
- Find the general solution of the differential equation: x² d²y/dx² − x dy/dx + 4y = x sin(log x). (7 marks, 2025, Cauchy-Euler Equation)
- Solve the following set of simultaneous linear differential equations: dx/dt = 3x + 8y; dy/dt = −x − 3y (7 marks, 2025, Linear ODE Constant Coefficients)
- Find the Particular Integral of (D² − 4D + 4)y = e^(2x) (2 marks, 2024, Linear ODE Constant Coefficients)
- Find the Complementary Function of (D³ + 2D² − 3D)y = 0 (2 marks, 2024, Linear ODE Constant Coefficients)
- Solve using method of variation of parameters: y'' + y = cosec x (7 marks, 2024, Variable Coefficient ODE)
- Solve: (D² − 4D + 4)y = 8x²e^(2x) sin 2x (7 marks, 2024, Linear ODE Constant Coefficients)
- Solve the simultaneous differential equations: dx/dt + 2x − 3y = 0; dy/dt − 3x + 2y = 0 (7 marks, 2024, Linear ODE Constant Coefficients)
- Solve: (D³ + 2D² − 3D)y = eˣ, D = d/dx (2 marks, 2023, Linear ODE Constant Coefficients)
- Solve the following differential equation: x² d²y/dx² + 2x dy/dx − 12y = x³ log x. (7 marks, 2023, Cauchy-Euler Equation)
Most asked Unit 1 topics
- Linear ODE Constant Coefficients – asked 14 times
- Variable Coefficient ODE – asked 6 times
- Cauchy-Euler Equation – asked 3 times
Unit 1 question pattern
- 2-mark questions: 13 asked in 2019–2025
- 7-mark questions: 9 asked in 2019–2025
- 10-mark questions: 12 asked in 2019–2025
- About 42 marks from Unit 1 in every paper
- 20 questions were asked again in a later year
Unit 1 questions year by year
- 2025: 5 Unit 1 questions asked (25 marks across that year's papers)
- 2024: 5 Unit 1 questions asked (25 marks across that year's papers)
- 2023: 4 Unit 1 questions asked (23 marks across that year's papers)
- 2022: 10 Unit 1 questions asked (68 marks across that year's papers)
- 2019: 10 Unit 1 questions asked (68 marks across that year's papers)