Question

$(x+3y+2)dy=(1+xy)dx$

Answer 1

Solution requires advanced techniques or software

Answer 2

This differential equation is non-linear and non-separable. It is not easily solved using standard methods for exact equations or integrating factors. Advanced techniques or software may be required to find a solution. The equation can be rewritten as:

$\frac{dy}{dx} = \frac{1+xy}{x+3y+2}$

Or as:

$x dy + 3y dy + 2 dy = dx + xy dx$

This form does not immediately suggest a standard solution method. Further analysis is needed to determine if there is a closed-form solution.