अवकल समीकरण `x^(2)(y+1)dx+y^(2)(x-1)dy=0` को हल कीजिये।

Explanation

`x^(2)(y+1)dx+y^(2)(x-1)dy=0`
`implies((x^(2))/(x-1))dx+((y^(2))/(y+1))dy=0`
`implies((x^(2)-1+1)/(x-1))dx+((y^(2)-1+1)/(y+1))dy=0`
`implies(x+1+(1)/(x-1))dx+(y-1+(1)/(y+1))dy=0`
समाकलन करने पर,
`int(x+1+(1)/(x-1))dx+int(y-1+(1)/(y+1))dy=0`
`implies(x^(2))/(2)+x+log(x-y)+(y^2)/(2)-y+log(y+1)=c`
`implies(1)/(2)(x^(2)+y^(2))+(x-y)+log(x-1)(y+1)=c`
`implies(1)/(2)(x^(2)+y^(2))+(x-y)+log(x-1)(y+1)=c`
`implies(x^(2)+y^(2))+2(x-y)+2log(x-1)(y+1)=k`
जबकि k स्वेच्छ अचर है।