6. Solving Differential Equations with a Change of Variable (I)

This chapter delves into the art of solving higher-order differential equations by reducing their order through strategic variable substitutions. It focuses on two primary cases: equations that do not explicitly contain the dependent variable and those that do not contain the independent variable. The chapter provides a step-by-step guide on how to transform these higher-order equations into first-order differential equations, making them easier to solve. It includes solved examples that illustrate the application of these methods, along with MATLAB implementations to verify the solutions. The chapter also explores special cases and provides a comprehensive set of solutions for various differential equations. By the end of the chapter, readers will have a solid understanding of how to approach and solve complex differential equations using variable substitution techniques.