Question

Solution of the differential equation `x(dy/dx)^2 + 2sqrt(xy) dy/dx + y = 0` is ______

Options

• x + y = a

• `sqrtx - sqrty = sqrta`

• `sqrtx + sqrty = sqrta`

• `x^2 + y^2 = a^2`

Answer 1

`underline(sqrtx + sqrty = sqrta)`

Explanation:

`x(dy/dx)^2 + 2sqrt(xy) dy/dx + y = 0`

⇒ `(sqrtxdy/dx + sqrty)^2 = 0`

⇒ `sqrtxdy/dx + sqrty = 0`

Integrating on both sides, we get

`intdy/sqrty + intdx/sqrtx = c`

⇒ `2sqrty + 2sqrtx = c`

⇒ `sqrtx + sqrty = sqrta`, where `sqrta = c/2`