A solution curve of the differential equation \( \mathrm{P} \) \( \left(x^{2}+x y+4 x+2 y+4\righ...

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A solution curve of the differential equation
\( \mathrm{P} \) \( \left(x^{2}+x y+4 x+2 y+4\right) \frac{d y}{d x}-y^{2}=0, x0 \), passes through the point \( (1,3) \). Then the solution curve
[JEE Advanced-2016]
(a) intersects \( y=x+2 \) exactly at one point
(b) intersects \( y=x+2 \) exactly at two points
(c) intersects \( y=(x+2)^{2} \)
(d) does NOT intersect \( y=(x+3)^{2} \)
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