अवकल समीकरण `(dy)/(dx)=sqrt((1+y^2)/(1+x^2))`को हल कीजिए -

Explanation

`(dy)/(dx)=sqrt((1+y^(2))/(1+x^(2)))`
या `(dy)/(sqrt(1+y^(2)))=(dx)/(sqrt(1+x^(2)))`
दोनों पक्षों का समाकलन करने पर
`int (dy)/(sqrt(1+y^(2)))=int (dx)/(sqrt(1+x^(2)))`
`int (sec^(2) phi d phi)/(sqrt(1+tan^(2) phi))=int (sec^(2)theta d theta)/(sqrt(1+tan^(2)theta))" "` माना `x= tan theta`
`int sec phi d phi =int sec theta d theta" " dx=sec^(2) theta d theta`
`" "` तथा `y=tan phi`
`log (Sec phi + tan phi)=log (sec theta + tan theta)+c" " dy=sec^(2) phi d phi`
या `log (sqrt(1+y^(2))+y)=log (sqrt(1+x^(2))+x)=c`
या `log ""((sqrt(1+y^(2))+y))/((sqrt(1+x^(2))+x))=c`