Question

The equation of the curve that passes through the point (1,2) and satisfies the differential equation $\frac{dy}{dx}=\frac{-2xy}{(x^2+1)}$ is

• A. $y(x^2+1)=4$
• B. $y(x^2+1)+4=0$
• C. $y(x^2-1)=4$
• D. $Noneofthese$

Answer 1

The correct option is A $y(x^2+1)=4$

$\frac{dy}{dx}=\frac{-2xy}{(x^2+1)}\Rightarrow \frac{dy}{y}=-\frac{2x}{x^2+1}dx$
On integrating, we get
$logy=-log(1+x^2)+logc\Rightarrow y(1+x^2)=c$
Since curve passes through (1, 2), we have
$c=2(1+1^2)\Rightarrow c=4$
Hence solution is $y(x^2+1)=4$