$\mathrm{P}=2 \mathrm{P}+2 \mathrm{x} \frac{\mathrm{dP}}{\mathrm{dx}}+2 \mathrm{xP}^{4}+4 \mathrm{P}^{3} \mathrm{x}^{2} \frac{\mathrm{dP}}{\mathrm{dx}}$
$\Rightarrow 0=\mathrm{P}\left(1+2 \mathrm{xP}^{3}\right)+2 \mathrm{x} \frac{\mathrm{dP}}{\mathrm{dx}}\left(1+2 \mathrm{P}^{3} \mathrm{x}\right)$
$\Rightarrow \mathrm{P}+2 \mathrm{x} \frac{\mathrm{dP}}{\mathrm{dx}}=0 \Rightarrow 2 \frac{\mathrm{dP}}{\mathrm{p}}=-\frac{\mathrm{dx}}{\mathrm{x}}$
$\Rightarrow 2 \log \mathrm{P}+\log \mathrm{x}=$ constant
$\Rightarrow \mathrm{P}^{2} \mathrm{x}=\mathrm{C} \Rightarrow \mathrm{P}=\sqrt{\mathrm{C} / \mathrm{x}}$
Substituting this value in the given equation, we
get $y=2 \sqrt{C x}+C^{2}$
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