Mathematics-IV Unit 1 Notes AKTU (BAS303)

AKTU · BTECH · Semester 3, 4 · Mathematics-IV · Unit 1 · Notes

AKTU Mathematics-IV (BAS303) Unit 1 notes for B.Tech Semester 3/4 – Partial Differential Equations. Topics: Origin of PDE, Lagrange's Linear PDE Method…

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Unit 1: Partial Differential Equations – AKTU syllabus topics

  • Origin of PDE
  • Lagrange's Linear PDE Method: Formation of Linear PDE, Solving Lagrange's Equation
  • Charpit's Non-Linear PDE Method
  • Higher Order Linear PDE: Constant Coefficients PDE, Reducible to Constant Coefficients

Most asked AKTU PYQ questions from Unit 1

  1. Q3a. Solve the Partial Differential Equation: (𝐷² − 𝐷𝐷′ − 1)(𝐷 − 3𝐷′ + 2)𝑧 = x⁴ + 4xy + 2y². (10 marks, 2020-21)
  2. Q3b. Solve: (𝑥² + 𝑦² + 𝑦𝑧)𝑝 + (𝑥² + 𝑦² − 𝑧𝑥)𝑞 = 𝑧(𝑥 + 𝑦). (10 marks, 2020-21)
  3. Q2a. Solve (𝑥² + 2xy − 𝑦²)𝑝 + (𝑦² + 2xy − 𝑥²)𝑞 = 𝑥² − 𝑦². (10 marks, 2020-21)
  4. Q2a. Find the general solution of the partial differential equation (y + z)p + (z + x)q = (x + y). (10 marks, 2022-23)
  5. Q3a. Solve: (mz - ny)p + (nx - lz)q = ly - mx. (10 marks, 2022-23)
  6. Q3a. Solve (y + zx)p - (x + yz)q = x² - y². (10 marks, 2021-22)
  7. Q1a. What is the auxiliary equation of Charpit Method? (2 marks, 2020-21)
  8. Q3a. Find the solution of the partial differential equation [2D² + 5DD' + 3(D')²]z = eˣ. (10 marks, 2022-23)
  9. Q3b. By Charpit's method, find the complete solution of PDE: px + qy - pq = 0. (10 marks, 2022-23)
  10. Q2a. Solve the following partial differential equation by Charpit Method: px + qy = pq. (10 marks, 2021-22)

AKTU paper codes: BAS303, BAS303H, BAS403, BAS403H, KAS302, KAS402

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