Differential equations are essential tools for modeling real-world phenomena in physics, engineering, biology, and economics. This course begins by explaining what differential equations are, exploring their order, degree, and types of solutions. Learners will understand how differential equations are formed and the different classifications that guide solution methods.

The course then focuses on various solution techniques for first order differential equations. You will learn to solve separable equations through step-by-step examples and tackle initial value problems to understand their practical applications. Techniques for reducing complex equations to separable forms are covered, along with the concept of homogeneous functions and how they relate to solving differential equations.

Further, the course introduces exact differential equations, offering multiple examples that clarify their identification and solution processes. Integrating factors, a powerful tool for solving non-exact equations, are explained with clear rules and demonstrations. By combining these methods, students will develop a comprehensive skill set to solve a broad range of first order differential equations effectively.