अवकल समीकरण `(x+y)(dx-dy)=dx+dy` का हल क्या है?

Options

A. `x+y = c.e ^(x-y)`
B. `x-y = c.e ^(x-y)`
C. `x+y = c.e ^(x+y)`
D. इनमे से कोई नहीं

Answer

A

Explanation

दिया है, (x+y)(dx-dy) = (dx+dy)
implies (x+y)dx-(x+y) dy = dx + dy
`implies (x+y-1)dx=(x+y+1)dy`
`implies (dy)/(dx)=(x+y-1)/(x+y+1)`
माना `v=x+yimplies(dv)/(dx)=1+(dy)/(dx)`
`implies (dv)/(dx)=1+(v-1)/(v+1)=(2v)/(v+1)implies(v+1)/(2v)dv=dx`
`implies int((1)/(2)+(1)/(2v))dv=intdx`