हल कीजिए
`(x+y) ^(2)(dy)/(dx) =a^(2)`

Explanation

दिया गया अवकल समीकरण है. `(x+y) ^(2)(dy)/(dx)=a^(2)`
`implies(dy)/(dx)= (a^(2))/((a+y)^(2))" "...(1)`
माना `x+y =v" "...(2)`
x के सापेक्ष अवकलन करने पर,
`1+(dy)/(dx)=(dv)/(dx)`
`implies(dy)/(dx) =(dv)/(dx)-1" "...(3)`
समी (1 ) (2 ) और (3 ) से,
`(dv)/(dx)-1(a^(2))/(v^(2))`
`implies(dv)/(dx)=(a^(2))/(v^(2))+1`
`implies (dv)/(dx) =(a^(2)+v^(2))/(v^(2))`
`implies (v^(2))/(a^(2)+v^(2)) dv =dx,` (चरो के पृथक्करण से)
समाकलन करने पर,
`int (v^(2))/(a^(2)+ v^(2))dv=int dx `
`impliesint ((a^(2) +v^(2))-a^(2))/(a^(2)+v^(2))dv = intdx`
`implies int (1-(a^(2))/(a^(2)+ v^(2)))dv = x+C`
`implies int 1 dv -a^(2) int (1)/(a^(2)+v^(2))dv= x+C`
`impliesv -a^(2) xx1/a tan ^(-1) ((v)/(a))=x+C`
`implies v- tan^(-1) ((v)/(a))=x+C`
`implies y-a tan ^(-1) ((x+y)/(a))=C.`