Question

Assertion :Solution of $ydx-xdy+x^2{y}^{2}dx=0$ is $3x+x^{3}y=kx$, where k is any constant Reason: $\frac{ydx-xdy}{y^2}=d\left(\frac{x}{y}\right)$

• 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. Assertion is incorrect and Reason are correct

Answer 1

The correct option is D Assertion is incorrect and Reason are correct

Reason is true
Assertion:
$ydx-xdy+x^2{y}^{2}dx=0$
$\Rightarrow$ $\frac{ydx-xdy}{y^2}+x^{2}dx=0$ $\Rightarrow$ $d\left(\frac{x}{y}\right)+d\left(\frac{x^3}{3}\right)=0$
on integrating both sides
$\Rightarrow$ $\frac{x}{y}+\frac{x^3}{3}=c$

$\Rightarrow$ $3x+x^{3}y=ky$