Solve the following differential equation \((x^2-yx^2)dy+(y^2+xy^2)dx=0\)Solution : Separating the variables, the given equation can be written as :\(\square\,dy+\square\,dx=0\)\(\therefore\left(y^{-2}-\frac{1}{y}\right)dy+\left(x^{-2}+\frac{1}{x}\ri…

Q.3 (C) (ii) Solve the following differential equation \((x^2-yx^2)dy+(y^2+xy^2)dx=0\)

Solution : Separating the variables, the given equation can be written as :

\(\square\,dy+\square\,dx=0\)
\(\therefore\left(y^{-2}-\frac{1}{y}\right)dy+\left(x^{-2}+\frac{1}{x}\right)dx=0\)
\(\square\,dy-\frac{1}{y}dy+x^{-2}dx+\square\,dx=0\)
Integrating we get,
\(\int y^{-2}dy-\int\frac{1}{y}dy+\int x^{-2}dx+\int\frac{1}{x}dx=0\)
\(\therefore\frac{y^{-1}}{-1}-\square+\frac{x^{-1}}{-1}+\square=c\)
\(-\frac{1}{y}-\frac{1}{x}+\log x-\log y=c\)
\(\log x-\log y=\square+c\)
is the required solution.