Question

The solution to the differential equation $y\,log\,y+xy'=0$, where $ y (1) = e$, is

• A. $x(log\,y)=1$
• B. $xy(log\,y)=1$
• C. $(log\,y)^{2}=2$
• D. $log \,y+\left(\frac{x^{2}}{2}\right)y=1$

Answer 1

Answer: (A)

$x \frac{dy}{dx}+y (log\,y)=0$
or $\int \frac{dx}{x}+\int \frac{dy}{y\left(log\,y\right)}=c$
or $log\,x+log(log\,y)=log\,c$
or $x\,log\,y=c$
$y (1)=e$
$\Rightarrow c=1$
Hence, the equation of the curve is $x \,log \,y = 1$