The differential equation obtained by eliminating the arbitrary constants a and b from ` xy = ae^(x) + be^(-x) ` is

Options

A. ` x(d^(2)y)/(dx^(2)) +2(dy)/(dx) -xy =0`
B. ` (d^(2)y)/(dx^(2))+2y(dy)/(dx) -xy =0`
C. ` x (d^(2)y)/(dx^(2)) +2 (dy)/(dx)+xy = 0 `
D. ` (d^(2)y)/(dx^(2)) +(dy)/(dx) - xy = 0 `

Answer

a

Explanation

Given , `xy + ae^(x) + be^(-x)" " ` …(i)
On differentiating w.r.t.'x' , we get
` rArr x (dy)/(dx) + y = ae^(x) - be^(-x)" "` ...(i)
` rArr x (d^(2)y)/(dx^(2)) +(dy)/(dx) +(dy)/(dx) = ae^(x) +be^(-x)`
` rArr x (d^(2)y)/(dx^(2))+2 (dy)/(dx) - xy =0` [ from Eq. (i)]