Given that dy/dx = μ(ax+by+c), where μ is an arbitrary function and a,b,c are constants. Find the solution of the differential equations. Hence and otherwise, solve dy/dx = (x+y+1)² - 2

Question

Given that dy/dx = μ(ax+by+c), where μ is an arbitrary function and a,b,c are constants. Find the solution of the differential equations. Hence and otherwise, solve dy/dx = (x+y+1)² - 2

Answer 1

This is an excellent article on solving Riccati equations.

https://math.stackexchange.com/questions/462075/how-to-solve-the-riccatis-differential-equation

Follow its methods to learn that your equation has solution

y = 1/(c*e^(2x) + 1/2) - x - 2