AMS 361: Applied Calculus IV Homework 2 Solved

AMS 361: Applied Calculus IV 
Homework 2 

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.