Semester 2 का पहला Lecture

Introduction

• Welcome everyone
• Start of the Semester 2 studies
• Subject of Differential Equations

Importance of Differential Equations

• First order and first degree Differential Equations
• Review of subjects studied in 12th grade
• Difference between General Solution and Particular Solution
• Use of Differential Equations in Engineering

Types of Differential Equations

• Exact Equations and Non-Exact Equations
• Methods for finding the General Solution

• Format of Differential Equations:

  ( \frac{dy}{dx} + f(x) + g(y) = 0 )

  ( Mdx + Ndy = 0 )

Identification of Exact Differential Equations

• Check ( \frac{\partial M}{\partial y} ) and ( \frac{\partial N}{\partial x} )

Determining the General Solution

• To find the General Solution:
  • ( \int Mdx + \int N \text{ (terms in } N \text{ free from } x) dy = C )

Example

• In the first example, Differential Equation given is:
  ( tan(y) dy + x dx = 0 )
• The General Solution for this must be found

Important Formulas

• Formula for the General Solution:
  • ( \int Mdx + \int Ndy = C )

Questions and Answers

• Asked questions to students
• Encouraged everyone to clear their doubts

Homework

• Some questions have been given to students which they have to solve themselves

Conclusion

• Appealed to everyone to keep meeting in the next lecture
• Urged to share with friends