12. Bernoulli’s Equation

Dive into the world of Bernoulli's equation, a first-order nonlinear differential equation with the form y' + p(x)y = q(x)yn, where n is any real number except 0 or 1. This chapter explores the transformation of nonlinear Bernoulli's equations into linear forms through clever substitutions, making them easier to solve. Through a series of solved examples, you'll learn how to tackle various forms of Bernoulli's equation, including those with specific values of n. The chapter also demonstrates the use of MATLAB for symbolic computation, providing practical solutions to differential equations. Discover how to verify solutions and explore the equivalence of different forms. Whether you're dealing with complex-valued functions or seeking to understand the underlying mathematics, this chapter offers a comprehensive guide to mastering Bernoulli's equation.