Question

Assertion :The order of the differential equation, of which $xy=c{e}^x+b{e}^{-x}+x^2$ is a solution, is $2$ Reason: The differential equation is $x\frac{d^{2}y}{{dx}^2}+2\frac{dy}{dx}-xy+x^2-2=0$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

We have, $xy={ce}^x+{be}^{-x}+x^2$ ...(1)
Differentiating with respect to $x,$ we get
$x\frac{dy}{dx}+y={ce}^x-{be}^{-x}+2x$ ...(2)
Differentiating again,
$x\frac{d^{2}y}{{dx}^2}+2\frac{dy}{dx}{ce}^x-{be}^{-x}+2=xy-x^2+2$ [Using (1)]
Hence, the required differential equation is
$x\frac{d^{2}y}{{dx}^2}+2\frac{dy}{dx}-xy+x^2-2=0.$
The order of this differential equation is $2.$