Question

The solution of $xdx+ydy=x^{2}ydy-x{y}^{2}dx$ is

• A. $x^2-1=c(1+y^2)$
• B. $x^2+1=c(1-y^2)$
• C. $x^3-1=c(1+y^3)$
• D. $x^3+1=c(1-y^3)$

Answer 1

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

$\Rightarrow xdx+x{y}^{2}dx=x^{2}ydy-ydy$
$\Rightarrow x(1+y^2)dx=y(x^2-1)dy$
$\Rightarrow \int \frac{2xdx}{x^2-1}\int \frac{2y}{1+y^2}dy+c$
$\Rightarrow log(x^2-1)=log(1+y^2)+logc$
$\Rightarrow (x^2-1)=(1+y^2)c$