I want to solve Equation (1). w is a constant:
\begin{eqnarray} \text{Equation (1): }\frac{dx}{dt}=1+x^2w^2\end{eqnarray}
and I have been told that it is solved by (2):
\begin{eqnarray} \text{Equation (2): }x(t)=\frac{Ax(0)+B}{Cx(0)+D}\end{eqnarray}
Problem
I believe them, but before I keep...