Direction field of complicated equations

Question

I have the following differential equation I would like to graph differential equation: dy/dx = \frac{2x}{x^4+1}. I would also like to graph the solution that goes through the point (1,1). Here's what I currently have:

\documentclass{report}
\usepackage{tikz}
\usepackage{pgfplots}
\usepgfplotslibrary{external}
\tikzexternalenable
\begin{document}
\begin{tikzpicture}[declare function={f(\x)=2*\x/(\x^4+1);}]
  \begin{axis}[
    xmin=-4,xmax=4,
    ymin=-4,ymax=4,
    domain=-4:4,
    ]
\def\xmax{4} \def\xmin{-4}
\def\ymax{4} \def\ymin{-4}
\def\nx{15}
\def\ny{15}
\def\yo{1}

\pgfmathsetmacro{\hx}{(\xmax-\xmin)/\nx}
\pgfmathsetmacro{\hy}{(\ymax-\ymin)/\ny}
\foreach \i in {0,...,\nx}
\foreach \j in {0,...,\ny}{
  \pgfmathsetmacro{\yprime}{f({\xmin+\i*\hx})}
  \addplot [blue,shift={({\xmin+\i*\hx},{\ymin+\j*\hy})}]
    (0,0)--($(0,0)!2mm!(.1,.1*\yprime)$);
}

\addplot [<->,red] {-1/4*pi+rad(atan(x^2))+1};

\end{axis}
\end{tikzpicture}
\end{document}

But I keep getting the following error:

! Missing number, treated as zero.
<to be read again> 
                   {
l.30     }
?

I originally had \pgfmathsetmacro{\yprime}{f({\xmin+\i*\hx},{\ymin+\j*\hy})} in replace of \pgfmathsetmacro{\yprime}{f({\xmin+\i*\hx})} because I don't need to pass in the \y since the function doesn't use it. But even when I do so and update the function definition from f(\x) = ... to f(\x,\y) = ..., the program still crashes giving:

! Undefined control sequence.
\pgfmath@dimen@ ...men@@ #1=0.0pt\relax \pgfmath@
l.32   \end{axis}
?

I'm aware of the following questions. I've used them and none of them worked out:

1. How to draw slope fields with all the possible solution curves in latex
2. How to plot a function and its derivative
3. Differential Equation direction plot with pgfplots