posted by sofia .
find the implicit function of x^3+3^y=3xy
Not sure if you can solve it explicitly. A 3-d plot is possible with most graphics software. The solution curve is given by the contour x^3+3^y-3xy=0.
See for example:
examine this closely.
3x^2 dx+3^y * ln3*dy=3y dx + 3x dy
dy/dx= 3(y-x^2) / (ln3*3^y -3x)
check my algebra, I gathered terms in my head.