In conclusion, differential equations are a powerful tool for modeling a wide range of phenomena in mathematics, physics, and engineering. The book by Maity Ghosh provides a comprehensive introduction to differential equations, including their types, solution methods, and applications. By mastering the concepts and techniques presented in this book, students and researchers can develop a deep understanding of differential equations and their role in modeling real-world phenomena.

If you recall the : [ M(x,y) , dx + N(x,y) , dy = 0 ] with condition: [ \frac\partial M\partial y = \frac\partial N\partial x ]

The solution to the homogeneous part.

If we replace p(x) with a piecewise function that jumps sign, the integrating factor still exists (as a piecewise exponential), but the solution may at a discontinuity point. This underscores why the continuity of (p) is crucial in Theorem 2.1.