Engineering Mathematics 1: Euler's Method and Solutions Analysis

This document provides a complete solution to an Engineering Mathematics assignment. The solution begins with solving a differential equation using separation of variables, finding both the general and exact solutions. It then applies Euler's method to approximate solutions, detailing the process and the use of different step sizes (h = 0.05, 0.1, 0.2, and 0.5) to estimate y values from x = 0 to x = 5. The assignment includes a comparison of approximate and exact values, with error analysis presented in a spreadsheet format. The document analyzes the impact of step size on accuracy and provides a chart illustrating the approximate and exact y values versus x values. The analysis highlights that a smaller step size yields a more accurate approximation, with h=0.1 offering the closest result to the exact solution.