Briefly. Ahsan includes Laplace transforms as a method for solving ODEs with discontinuous forcing functions. However, for an exhaustive treatment of Laplace and Fourier transforms, you would need a supplementary text (like a dedicated engineering math book).
"Differential Equations and Their Applications" by Zafar Ahsan is a thorough and well-structured book that covers the fundamental concepts of differential equations and their applications in various fields. The book is designed for undergraduate and graduate students, researchers, and professionals seeking to understand the principles and applications of differential equations. Briefly
The book is currently in its 3rd edition (published by PHI Learning in 2016). Briefly