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'.
Find an equation of tangent line:
x+1=(x+4y)/(2x+y^3) at (0,2).
Doing everything I got
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.