We need to find y when `x = 2`.

On substituting, we have:

`2(y)+y^2=4`

Solving for `y` using the quadratic formula gives:

`y^2 +2y - 4=0`

`y=(-2+- sqrt(2^2 + 16))/2`

`y=-1 +- sqrt(5)`

Now, since the question says `y > 0`, we choose `y=-1+sqrt(5)=1.236` only.

Using the result from the first part of the question:

`(d^2y)/(dx^2)=(2y(x+y))/((x+2y)^3)`

We substitute and obtain:

`=(2(1.236)(2+1.236))/((2+2(1.236))^3)`

`=(2(1.236)(2-3(1.236)))/((2+2(1.236)^3)`

`=0.0894`

Video

Here is a movie of the solution. The form of the second derivative here is different to the above solution, but is also quite correct.