Solve dθ/dx=tan^-1(ax/x^2+h(a+h))

$$\frac { d \theta } { d x } = \tan ^ { - 1 } ( \frac { a x } { x ^ { 2 } + h ( a + h ) } )$$

Solve for a

$$\left\{\begin{matrix}a=0\text{, }&x\neq 0\\a\neq -h\text{, }&x=0\text{ and }h\neq 0\end{matrix}\right.$$

Solve for h

$$\left\{\begin{matrix}h\in \mathrm{R}\setminus (\frac{|a|-a}{2},\frac{-|a|-a}{2}\cup (-\infty,-a)\text{, }a>0\cup (-\infty,0)\text{, }a<0\cup (-\infty,-a]\cup (-a,\infty)\text{, }a<0\cup [0,\infty))\text{, }&a>0\text{ and }x=0\text{ and }h\neq 0\text{ and }a\neq -h\\h\in \mathrm{R}\setminus (\frac{|a|-a}{2},\frac{-|a|-a}{2}\cup (-\infty,0]\cup (-\infty,-a)\text{, }a>0\cup (0,\infty)\text{, }a>0\cup [-a,\infty))\text{, }&a<0\text{ and }x=0\text{ and }h\neq 0\text{ and }a\neq -h\\h\in (-\infty,\frac{-|a|-a}{2})\cup (\frac{|a|-a}{2},\infty)\text{, }&a\neq 0\text{ and }x=0\text{ and }h\neq 0\text{ and }a\neq -h\\h\neq 0\text{, }&a=0\text{ and }x=0\text{ and }h\neq 0\\h\in \mathrm{R}\text{, }&a=0\text{ and }x\neq 0\end{matrix}\right.$$