(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The problem and its answers are attached.

I prefer the first one as (same thing but isolated for y):

y_1(x) = [k_1 * x + x * ln(x)]/[k2 - ln(x)]

2. Relevant equations

First order homogeneous differential equation.

y = xv, dy/dx = v + x dv/dx

3. The attempt at a solution

I solved this successfully. Given that at some point in the solution of the problem for solving y_1(x), I get a denominator with (x+y), it is my "mathematical duty" to check if x + y = 0 => y = -x is a solution to the differential equation and it is. Because of the nature in which I got this y = -x solution, I am confused as to whether I treat this as one of the two alternatives for a general solution or both together span the one and only general solution.

Any input would be greatly appreciated!

Thanks in advance!

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# Homework Help: Are these two general solutions or one general/two particular solutions?

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