[SOLVED] AMS361-Homework 2

Description

Problem 2.1 Find the G.S. of the Riccati DE:

𝑥²𝑦^′ + (𝑥𝑦)² − 2 = 0

Problem 2.2 Find the G.S. of the Riccati DE:

𝑥³𝑦^′ + 𝑥²𝑦 − 𝑦² = 2𝑥⁴

given that 𝑦₁ = 𝑐𝑥² is a solution.

Problem 2.3 Find the G.S. of the DE:

𝑥²𝑦^′ + 6𝑥²𝑦² − 1 = 0

(hint: substituting 𝑦 = 1/𝑧.)

Problem 2.4 Solving the following IVP:

1                                                                  𝑦2

^{𝑦′ = cos𝑥 − 2sin𝑥tan𝑥 + 2cos𝑥

𝑦(𝑥 = 0) = 2019

Given that 𝑦₁ = sin𝑥 is a solution.