Question

A solution of the differential equation $ \left(\frac{dy}{dx}\right)^{2}-x\frac{dy}{dx} + y = 0 $ is

• A. $ y = 2x $
• B. $ y = -2x $
• C. $ y = 2x-4 $
• D. $ y = 2x+4 $

Answer 1

Answer: (C)

Let $y=2 x-4$ be a solution of the differential equation
$\left(\frac{d y}{d x}\right)^{2}-x\left(\frac{d y}{d x}\right)+y=0$
Now, we cross check this solution
LHS $\left(\frac{d y}{d x}\right)^{2}-x\left(\frac{d y}{d x}\right)+y $
$=\left\{\frac{d}{d x}(2 x-4)\right\}^{2}-x\left\{\frac{d}{d x}(2 x-4)\right\}+(2 x-4)$
$=(2)^{2}-x(2)+2 x-4 $
$=4-2 x+2 x-4 $
$=0=$ RHS
$\therefore y=2 x-4 $ be a required solution.