अवकल समीकरण `(1-y^(2))(dx)/(dy)+yx=ay(-1ltylt1)` का समाकलन गुणक है :

Options

A. `(1)/(y^(2)-1)`
B. `(1)/(sqrt(y^(2)-1))`
C. `(1)/(1-y^(2))`
D. `(1)/(sqrt(1-y^(2)))`

Answer

D

Explanation

दिया गया अवकल समीकरण
`(1-y^(2))(dy)/(dx)+yx=ay`,
`implies (dy)/(dx)+((y)/(1-y^(2)))x=(ay)/(1-y^(2))`
यहाँ, `P=(y)/(1-y^(2)),Q=(ay)/(1-y^(2))`
`I.F.=e^(int(y)/(1-y^(2))dx)`
`implies I.F.=e^(-(1)/(2)int(-2y)/(1-y^(2))dy)`
`implies I.F.=e^((-1)/(2)log(1-y^(2)))`
`implies I.F.=e^(log(1-y^(2))^(-1//2))`
`=(1-y^(2))^(-1//2)=(1)/(sqrt(1-y^(2)))`