Solution of the differential equation
$x\left(\frac{d y}{d x}\right)^2+2 \sqrt{x y} \frac{d y}{d x}+y=0$, is
Answer & explanation
Correct answer: option 4
We have,
$x\left(\frac{d y}{d x}\right)^2+2 \sqrt{x y} \frac{d y}{d x}+y=0$
$\Rightarrow \left(\sqrt{x} \frac{d y}{d x}+\sqrt{y}\right)^2=0$
$\Rightarrow \sqrt{x} \frac{d y}{d x}+\sqrt{y}=0$
$\Rightarrow \frac{1}{\sqrt{x}} d x+\frac{1}{\sqrt{y}} d y=0$
$\Rightarrow 2 \sqrt{x}+2 \sqrt{y}=C \Rightarrow \sqrt{x}+\sqrt{y}=\sqrt{a}$, where $\sqrt{a}=2 C$