Differential Equations 🌐

📝 Instructions

🧑‍🏫 For the Paper-Setter

🎓 For the Candidates

📝 Instructions

📋 Instructions for the Paper-Setter

The question paper will consist of three sections: A, B, and C. Sections A and B will have four questions each from their respective syllabus sections, while Section C will contain one compulsory question with eleven short answer-type questions covering the entire syllabus uniformly. - Sections A and B: Each question will carry 6 marks. - Section C: This section will carry 11 marks. ✍️

🖊️ Instructions for the Candidates

Candidates are required to attempt five questions in total, selecting two questions from each of Sections A and B, along with the compulsory question from Section C. 📘

📘 Syllabus

Section A 🔢

  1. First Order Differential Equations: Order and degree of a differential equation, homogeneous equations, equations reducible to homogeneous, exact equations, linear differential equations, and equations reducible to linear differential equations. 🔄
  2. Higher Order Differential Equations: Wronskian, solution of linear homogeneous and non-homogeneous differential equations of higher order with constant coefficients and variable coefficients. Methods: Differential operator method, Variation of Parameters. 📏

Section B 🌟

  1. Linear Non-Homogeneous Differential Equations: Linear equations with variable coefficients, Euler-Cauchy method.
  2. Series Solutions: Power series method, Frobenius method, Bessel equations, Legendre equations, and their solutions. Properties of Legendre and Bessel functions: recurrence relations, orthogonality, Rodrigue's formula. ✨

📚 Books Recommended

  1. George F. Simmons: 'Differential Equations with Applications and Historical Notes', CRC Press. 📖
  2. Rai Singh: 'Ordinary and Partial Differential Equations', S. Chand & Co., New Delhi. 📚
  3. Zafar Ahsan: 'Differential Equations and Their Applications', Prentice-Hall of India Pvt. Ltd. 📘
  4. I.L. Piaggio: 'An Elementary Treatise on Differential Equations', Barman Press. 🔢

📝 Previous Year Question Papers of Differential Equations