We need to get the equation in the form of a linear DE of order 1.

Expand the bracket and divide throughout by dx:

`2y-8x^2+x(dy)/(dx)=0`

Rearrange:

`x(dy)/(dx)+2y=8x^2`

Divide throughout by x:

`(dy)/(dx)+2/xy=8x`

Here, `P(x)=2/x` and `Q(x) = 8x`.

`"IF"=e^(intPdx)` `=e^(int2/xdx)` `=e^(2 ln\ x)` `=e^(ln\ x^2)` `=x^2`

Now

`Qe^(intPdx)=(8x) x^2=8x^3`

Applying the formula:

`ye^(intPdx)=intQe^(intPdx)dx+K`

gives:

`y\ x^2=int8x^3dx+K=2x^4+K`

Divide throughout by x2:

`y=2x^2+K/x^2`

Solving directly, using Scientific Notebook

Scientific Notebook cannot solve our original question:

`2(y-4x^2)dx+x\ dy=0`

We have to rearrange it in terms of `(dy)/(dx)` and then solve it using

Compute menu → Solve ODE...Exact