Select and write the correct answer from the given alternatives in each of the following :
The differential equation of ` y = c/x + c^(2)` is :

Options

A. `x^(4) [(dy)/(dx)]^(2) -x (dy)/(dx) = y`
B. `(d^(2)y)/(dx^(2)) + x (dy)/(dx) + y = 0`
C. ` x^(3) [(dy)/(dx)]^(2) + x (dy)/(dx) = y`
D. ` (d^(2)y)/(dx^(2)) + (dy)/(dx) - y = 0`

Answer

A

Explanation

Given, ` y = c/x +c^(2)`
Differentiating both sides of the equation w.r.t.x we get ,
`(dy)/(dx) = (-c)/x^(2)`
or ` c = - x^(2) (dy)/(dx)`
By squaring on both sides
or `c^(2) = x^(4) ((dy)/(dx))^(2)`
` :. " " y = - x (dy)/(dx) + x^(4) ((dy)/(dx))^(2)`