Question

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

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

Answer 1

The correct option is C

$y=2x–4$

Explanation for the correct option:

Step 1. Take option C, and Differentiate it with respect to $x$.

$y=2x–4$

$\Rightarrow \frac{dy}{dx}=2$

Given, ${\left(\frac{dy}{dx}\right)}^2-x\left(\frac{dy}{dx}\right)+y=0$ ……..(1)

Step 2. Put this value of $\frac{dy}{dx}$ in equation (1).

$\Rightarrow {\left(2\right)}^2-x\times 2+2x-4=0$

$\Rightarrow$ $4-2x+2x+y=0$

Therefore, $y=2x-4$ is satisfied.

Hence, Option ‘C’ is Correct.