I'm sure the problem is with the derivative.
Can you take it from here? I'm sure your problem was finding the correct derivative y'.
Question is,
Find an equation of tangent line:
x+1=(x+4y)/(2x+y^3) at (0,2).
Doing everything I got
y-2=-9/16 (x-0)
My steps to it took up half a page...I just can't type it all out. If my answer is incorrect, then I will so we can see where I went wrong. To me it was a hard and long problem.