Mathematics-IV Unit 1 – Partial Differential Equations: important questions for AKTU
Unit 1 (Partial Differential Equations) questions that AKTU repeats most often. This unit carries about 28 marks per paper. Start with the repeated questions, then the most asked topics.
Most repeated Unit 1 questions
- Solve the Partial Differential Equation: (𝐷² − 𝐷𝐷′ − 1)(𝐷 − 3𝐷′ + 2)𝑧 = x⁴ + 4xy + 2y². (10 marks, 2021, Higher Order Linear PDE) – also asked in 2022, 2023, 2024, 2025, 2026
- Solve: (𝑥² + 𝑦² + 𝑦𝑧)𝑝 + (𝑥² + 𝑦² − 𝑧𝑥)𝑞 = 𝑧(𝑥 + 𝑦). (10 marks, 2021, Lagrange's Linear PDE Method) – also asked in 2022, 2023, 2024, 2025, 2026
- Solve (𝑥² + 2xy − 𝑦²)𝑝 + (𝑦² + 2xy − 𝑥²)𝑞 = 𝑥² − 𝑦². (10 marks, 2021, Lagrange's Linear PDE Method) – also asked in 2022, 2023, 2024, 2025, 2026
Most important Unit 1 topic
- Higher Order Linear PDE (Unit 1: Partial Differential Equations) – asked 17 times in 2021, 2022, 2023, 2024, 2025, 2026
Most asked Unit 1 topics
- Higher Order Linear PDE – asked 17 times
- Lagrange's Linear PDE Method – asked 13 times
- Charpit's Non-Linear PDE Method – asked 10 times
More Unit 1 previous year questions
- What is a linear partial differential equation of first order? Write its general form. (2 marks, 2026, Origin of PDE)
- State Charpit's method and mention when it is used. (2 marks, 2026, Charpit's Non-Linear PDE Method)
- Solve the linear partial differential equation (y + z) ∂z/∂x + (x + z) ∂z/∂y = x + y using Lagrange's method. (7 marks, 2026, Lagrange's Linear PDE Method)
- Solve the non-linear partial differential equation p² + q² = z where p = ∂z/∂x, q = ∂z/∂y using Charpit's method. (7 marks, 2026, Charpit's Non-Linear PDE Method)
- Solve the partial differential equation (D² - 4DD' + 4D'²)z = e^(2x+y). (7 marks, 2026, Higher Order Linear PDE)
Unit 1 syllabus topics
- Origin of PDE
- Lagrange's Linear PDE Method
- Charpit's Non-Linear PDE Method
- Higher Order Linear PDE