Question

What is the general solution of the differential equation $x^{2}dy+y^{2}dx=0$?

• A. $x+y=c$ where $c$ is the constant of integration
• B. $xy=c$ where $c$ is the constant of integration
• C. $c(x+y)=xy$ where $c$ is the constant of integration
• D. None of the above

Answer 1

The correct option is C $c(x+y)=xy$ where $c$ is the constant of integration

$x^{2}dy{+y}^{2}dx=0$

$\Rightarrow \frac{dy}{y^2}+\frac{dx}{x^2}=0$

On integrating, we get

$\Rightarrow -\frac{1}{y}-\frac{1}{x}+\frac{1}{c}=0\Rightarrow c(x+y)=xy$
Option C is correct