Exercises: 1. Try solving Example 2 by using method 2. 2. Determine whether the following equation is exact. If it is, then solve it. a. (2x + y)dx + (x- 2y) dy = 0 b. (cos x cos y + 2x) dx – (sin x sin y + 2y) dy = 0 c. cos 0 dr - (r sin 0 – eº) de = 0 3. Given the differential equation (x – 2y) dx + (y – 2x) dy = 0 i. Show that the differential equation is exact. Hence, solve the differential equation by the method of exact equation. ii. Show that the differential equation is homogeneous. Hence, solve the differential equation by the method of homogeneous equation. Check the answer with 3i. 20

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.