Question

The solution of $\frac{dy}{dx}=\frac{x+x^2}{y-y^2}$ is:

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

Answer 1

Answer: (A)

$3(y^2-x^2)=2(x^3+y^3)+c$

$\frac{dy}{dx}=\frac{x+x^2}{y-y^2}$
$\int (y-y^2)dy=\int (x+x^2)dx+c$
$\frac{y^2}{2}-\frac{y^3}{3}=\frac{x^2}{2}+\frac{x^3}{3}+c$
$\Rightarrow 3(y^2-x^2)=2(x^3+y^3)+c$