- #1

- 2

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**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 solving it I want to know how one concludes that (1) is solved by (2). In order to get (2), should I integrate something like (3)? Is it some kind of ansatz that I should have known? ...

\begin{eqnarray} \text{Equation (3): }\frac{dx}{1+x^2w^2}=dt\end{eqnarray}

I don't know what is it that I should be looking for. Could I get a clue?

Thank you very much