The singular solution of the differential equation given in previous problem is :
Step-by-Step Solution
Key Concept: A singular solution of a differential equation is found by eliminating the parameter p from the condition dp/dx = 0 (obtained by differentiating the general solution form). Here, setting x + 1/p = 0 gives p = -1/x, which when substituted back into the original differential equation yields y + 1 = -log(-x).
Differentiating the given equation yields $\left(x + \frac{1}{p}\right)\frac{dp}{dx} = 0$. For a singular solution, $x + \frac{1}{p} = 0$, so $p = -\frac{1}{x}$. Substituting back into the original equation gives $y = -1 + \log(-x)$, or $y + 1 = -\log(-x)$.
Correct Answer: 4