Solving Riccati(?) Equation Solve an Ordinary Differential Equation:
$\frac{dx}{dt}=-x^2+1+t^2$
I suppose that it's a Riccati equation, but there is no given  $w(t)$, where $x(t)=w(t) + \frac{1}{u(t)}$ .
I've found out that $x_1=\frac{1}{C_1+t}$, and what should I do next? I'm not sure if it's the right way anyway. I should find the $w(t)$ but don't know how.
I will be gratefull for any help

Making the substitution 
$$
x = \frac{y'}{y}
$$
the new DE reads
$$
\frac{y''(t)-(1+t^2) y(t)}{y(t)} = 0
$$
or considering $y(t) \ne 0$
$$
y''(t)-(1+t^2) y(t)=0
$$
which is a linear DE.
