Problem 2.1 (25 points): Find the G.S. of the Riccati DE:
𝑥2𝑦′ + (𝑥𝑦)2 − 2 = 0
Problem 2.2 (25 points): Find the G.S. of the Riccati DE:
𝑥3𝑦′ + 𝑥2𝑦 − 𝑦2 = 2𝑥4
given that 𝑦1 = 𝑐𝑥2 is a solution.
Problem 2.3 (25 points): Find the G.S. of the DE:
𝑥2𝑦′ + 6𝑥2𝑦2 − 1 = 0
(hint: substituting 𝑦 = 1/𝑧.)
Problem 2.4 (25 points): Solving the following IVP:
1 𝑦2
{𝑦′ = cos𝑥 − 2sin𝑥tan𝑥 + 2cos𝑥
𝑦(𝑥 = 0) = 2019
Given that 𝑦1 = sin𝑥 is a solution.
