The solution of the differential equation `x^(4)(dy)/(dx)+x^(3)y+"cosec"(xy)=0` is equal to

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

` x^(4) (dy)/(dx) +x^(3) y + "cosec" (xy) = 0`
` rArr x^(4) dy + x^(3) y dx + "cosec" (xy) = 0`
` rArr x^(3) (x dy + y dx) + "cosec" (xy) dx= 0 `
` rArr x^(3) d (xy) + "cosec" (xy) dx = 0 `
` rArr (d(xy))/("cosec" (xy) )+ (dx)/(x^(3)) = 0`
On integrating both sides , we get
` int sin (xy) d (xy) + int x^(-3) dx = 0 `
` rArr - cos (xy) + ((x^(2))/-2)=C_(1)`
` rArr 2 cos (xy) +x^(-2) =C " " [ :' C = -2 C_(1)]`