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

Explanation

`(x-y^(2)x)dx-y(1-x^(2))dy=0`
`impliesx(1-y^(2))dx=y(1-x^(2))dx`
`implies(x)/(1-x^(2))dx=((y)/(1-y^(2)))dx`
`implies(xdx)/((1-x)(1+x))=(ydy)/((1-y)(1+y))`
`implies(1)/(2)[(1)/(1-x)-(1)/(1+x)]dx=(1)/(2)[(1)/(1-y)-(1)/(1+y)]dy`
समाकलन से
`impliesint((1)/(1+x)-(1)/(1-x))dx=int((1)/(1+y)-(1)/(1-y))dy`
`log(1+x)+log(1-x)=log(1+y)+log(1-y)+logc`
`implieslog(1-x^(2))=log(1-y^(2))+logc`
`implieslog((1-x^(2))/(1-y^(2)))=logc`
`implies(1-x^(2))=c(1-y^(2))` जबकि c स्वेच्छ अचर है।