अवकल समीकरण `(x+y)^(2)(dy)/(dx)=a^(2)` का हल है

Options

A. `y=atan^(-1)(x+y)+C`
B. `y=(1)/(a)tan^(-1)(x+y)+C`
C. `y=atan^(-1)((x+y)/(a))+C`
D. इनमे से कोई नहीं

Answer

C

Explanation

माना x + y = v तब,
`1+(dy)/(dx)=(dv)/(dx),(dy)/(dx)=(dv)/(dx)-1`
दिया हुआ समीकरण
`v^(2)((dv)/(dx)-1)=a^(2)impliesv^(2)(dv)/(dx)=v^(2)+a^(2)`
`implies (v^(2))/(v^(2)+a^(2))dv=dx`
`implies int(1-(a^(2))/(v^(2)+a^(2)))dv=intdx`
`implies v-a^(2)(1)/(a)tan^(-1).(v)/(a)=x+C`
`implies x+y-atan^(-1)((x+y)/(a))=x+C`
`y=atan^(-1)((x+y)/(a))+C`