Question

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

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

Answer 1

Answer: (C)

Given differential equation is
$(\frac{dy}{dx}{)}^2-x\frac{dy}{dx}+y=\mathrm{0...}(i)$
(a) $y=2\Rightarrow \frac{dy}{dx}=0$
On putting in Eq. (i), $0^2-x(0)+y=0$
$\Rightarrow y=0$ which is not satisfied.
(b) $y=2x\Rightarrow \frac{dy}{dx}=2$
On putting in Eq. (i),
$(2{)}^2-x.2+y=0$
$\Rightarrow 4-2x+y=0$
$\Rightarrow y=2x$ which is not satisfied
(c) $y=2x-4\Rightarrow \frac{dy}{dx}=2$
On putting in Eq. (i)
$(2{)}^2-2x+2x-4=0$
$4-2x+2x-4=0[\because y=2x-4]$
$y=2x-4$ is satisfied.
(d) $y=2x^2-4$
$\frac{dy}{dx}=4x$
On putting in Eq. (i),
$(4x{)}^2-x.4x+y=0$
$\Rightarrow y=0$ which is not satisfied.