A solution of the differential equation $\left(\frac{d y}{d x}\right)^2-x \frac{d y}{d x}+y=0$ is :
Answer & explanation
Correct answer: option 3
Let dy/dx = p
$\Rightarrow p^2 -xp+ y = 0$
$y = xp - x^2$
$\frac{dy}{dx}=(x-2p)\frac{dp}{dx}+p$
$\Rightarrow p = (x-2p)\frac{dp}{dx}+p$
$\frac{dp}{dx} = 0$
$\Rightarrow p = \text{ constant}$
$\Rightarrow y = xc - c^2$
From options , c = 2 , y = 2x-4