Find the general solution of each of the following differential equations:
`(x^(2)-yx^(2))dy+(y^(2)+xy^(2))dx=0`

Explanation

`x^(2)-yx^(2)) + (y^(2) +xy^(2))dx = 0`
` x^(2) (1-y) dy +y^(2) (1+x) dx =0`
` (1-y)/(y^(2) ) dy + (1 +x)/x^(2)dx =0`
Integrating we get ,
`int (1-y)/(y^(2))dy+ int(1+x)/x^(2) dx=c`
`int (1/y^(2) -1/y)dy + int (1/x^(2) + 1/x) dx =c `
` int y^(-2) dy - int 1/y dy + int x^(-2) dx + int 1/x dx = c `
` (y^(-1))/(-1) -log |y| + (x^(-1))/(-1) + log |x| =c`
` -1/y - log |y| - 1/x + |log |x|=c " " therefore log|x| - log |y| = 1/x + 1/y +c `
` log |x/y| = 1/x + 1/y +c`
This is the general solution.