दी गई अवकल समीकरण `x^(4)(dy)/(dx)+x^(3)y+cosec(xy)=0` का हल है

Options

A. `2 cos(xy)+x^(-2)=C`
B. `2cos(xy)+y^(-2)=C`
C. `2sin(xy)+x^(-2)=C`
D. `2sin(xy)+y^(-2)=C`

Answer

A

Explanation

माना xy = m
`y+x(dy)/(dx)=(dm)/(dx)" ...(i)"`
दिया है, `x^(4)(dy)/(dx)+x^(3)y+cosec(xy)=0`
`implies x^(3)(x(dy)/(dx)+y)+cosec(xy)=0`
`implies x^(3)(dm)/(dx)+cosec(xy)=0`
`implies x^(3)dm=-cosec(m)dx`
`implies -(1)/(cosec m)dm=(1)/(x^(3))dx`
दोनों पक्षों का समिकलन करने पर,
`-int(1)/(cosecm)dm=intx^(-3)dx`
`implies-intsin m dm=underset(-2)intx^(-3)dx`

`implies cosm=(x^(-2))/(-2)+C`
`implies 2cosm+x^(-2)=C`
`implies 2cos xy+x^(2)=C`