Question

The solution of
$(x^2-y{x}^2)\frac{dy}{dx}+(y^2+x^2{y}^2)=0$

• A. $log\left(xy\right)=\frac{1}{x}+\frac{1}{y}+c$
• B. $logy+\frac{1}{y}=x-\frac{1}{x}+c$
• C. $y-\frac{1}{y}=x-\frac{1}{x}+c$
• D. $logx+\frac{1}{x}=y-\frac{1}{y}+c$

Answer 1

The correct option is B $logy+\frac{1}{y}=x-\frac{1}{x}+c$

$(x^2-y{x}^2)\frac{dy}{dx}+(y^2+x^2{y}^2)=0$
$x^2(1-y)\frac{dy}{dx}+y^2(1+x^2)=0$
$x^2(1-y)\frac{dy}{dx}=-y^2(1+x^2)$
$\frac{(1-y)}{y^2}dy=-\frac{(1+x^2)}{x^2}dx$
$\int \frac{(1-y)}{y^2}dy=-\int \frac{(1+x^2)}{x^2}dx$
$\log y+\frac{1}{y}=x-\frac{1}{x}+c$
Hence, option 'B' is correct.