Lecture
This lecture focuses on the numerical resolution of a Cauchy problem using the method of separation of variables. The instructor presents a typical differential equation, which involves separating variables to facilitate finding an explicit solution. The equation is transformed and integrated, leading to the general solution of the problem. The instructor emphasizes the importance of initial conditions in determining the constant in the solution. The lecture also discusses the intervals in which the solution is defined, highlighting the distinction between local and global solutions. The instructor concludes by establishing the conditions under which the solution remains valid, ensuring that the function does not reach undefined values. This comprehensive approach provides a clear understanding of solving differential equations through practical examples and theoretical foundations.