Question 749772
Here is my solution:

{{{ (x^2 + 4)*(dy/dx) = 6*x*y }}}  ------- (1)


Rearranging the equation, we get:

{{{ (dy/y) = 6*x/(x^2+4)*dx }}}  ------- (2)


Replacing {{{x*dx}}} with {{{d(x^2+4)/2}}}, we get:

{{{ (dy/y) = 3/(x^2+4)*d(x^2+4)) }}} ------- (3)

Integrating both sides of the equation, we get:

{{{ int(dy/y) }}} = {{{int(3/(x^2+4)*d(x^2+4)) ) }}}

{{{ ln(y) = 3* ln(x^2+4) }}}  -------- (4)

This expression can be simplified into:

{{{ y = (x^2+4)^3 }}}  

I think this is the solution to the problem. I have checked the solution by differentiating it with respect to x. The end result is exactly the same as the equation given in the question:

{{{ y = (x^2+4)^3 }}} 
{{{ dy/dx = 3*(x^2+4)^2 }}} 
{{{ dy/dx = 3*(x^2+4)^3/(x^2+4) }}} 

Replacing {{{(x^2+4)^3}}} with {{{y}}}, we get:
{{{ dy/dx = 3*y/(x^2+4) }}} 

Rearranging the equation, we get an equation exactly exactly the same as the equation given in the original question:

{{{ (x^2 + 4)*(dy/dx) = 6*x*y }}}