From the differential equation by eliminating A and B in `Ax^(2)+By^(2)=1`

Options

A. ` x (d^(2)y)/(dx^(2)) +x((dy)/(dx))^(2)-y =0`
B. ` x(d^(2)y)/(dx^(2))+x(dy)/(dx)-y=0`
C. ` xy(d^(2)y)/(dx^(2))+x((dy)/(dx))^(2)-y(dy)/(dx)=0`
D. None of the above

Answer

c

Explanation

Given that , `Ax^(2) +BY^(2) = 1" " ` …(i)
On differentiate w.r.t .x, we get
` 2 Ax + 2By (dy)/(dx) =0`
` rArr A x + By (dy)/(dx) = 0" " ` …(ii) ltbr gt Again , on differentiate w.r.t x, we get
` rArr A+B { y (d^(2)y)/(dx^(2)) +(dy)/(dx) * (dy)/(dx)}=0" "` ... (iii) On multiplying Eq. (iii) by x and subtracting Eq. (ii), we get
` B { xy (d^(2)y)/(dx^(2))+ x ((dy)/(dx))^(2) } - By(dy)/(dx) = 0`
` rArr { xy (d^(2)y)/(dx^(2)) + x ((dy)/(dx))^(2) - y (dy)/(dx)}= 0 " " [ :' B != 0]`
` :. xy (d^(2)y)/(dx^(2)) + x((dy)/(dx))^(2) - y (dy)/(dx) = 0 `
which is the required differentil equation .