Analytic solution of a Graetz bridge rectifier with inductive filter
There are two things that you will have to address to find an analytic solution to your problem. First, the forcing function you are using is not taking into account the rectification from your ideal diodes, i.e., the function you should be using for your forcing function is a rectified sine. You can either use:
\begin{equation}
g(t) = |\sin(t)|,
\end{equation}
or,
\begin{equation}
\begin{split}
 g(t) &amp;= \sin(t) \qquad t\in [0,\frac{T}{2}) \\
&amp;= -\sin(t) \qquad t\in[\frac{T}{2},T].
\end{split}
\end{equation}

You could also set this up as an alternating series, but I think using the absolute value function as your forcing function and making a periodic extension of the result will be the easiest.

Second, I'm not familiar with LTSPICE, but you have your voltage source set as \$\sin(t)\$, you could replace it with a current source instead (if that option is available). So your initial condition \$i(t) = 0\$ is not correct.