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

Options

A. `x+y=a`
B. `sqrt(x)-sqrt(y)=sqrt(a)`
C. `x^(2) + y^(2) = a^(2)`
D. `sqrt(x)+sqrt(y)=C`

Answer

d

Explanation

Given , ` x ((dy)/(dx))^(2) + 2sqrt(xy) (dy)/(dx) + y = 0`
` rArr (sqrt(x) (dy)/(dx) + sqrt(y)^(2)) = 0`
` rArr 1/(sqrt(y))dy + 1/(sqrt(x)) dx = 0 `
` rArr 2 sqrt(2) + 2sqrt(2) = C_(1)`
` rArr sqrt(x) + sqrt(y) = C " " [ :' C = 1/2 C_(1)] `