  In this paper, we study anisotropic universe using Noether symmetries in
modified gravity. In particular, we choose locally rotationally symmetric
Bianchi type-$I$ universe for the analysis in $f(R,\mathcal{G})$ gravity, where
$R$ is the Ricci scalar and $\mathcal{G}$ is the Gauss-Bonnet invariant.
Firstly, a model $f(R,\mathcal{G})=f_0R^l+f_1\mathcal{G}^n$ is proposed and the
corresponding Noether symmetries are investigated. Further, we have also
recovered the Noether symmetries for $f(R)$ and $f(\mathcal{G})$ theories of
gravity. Secondly, some important cosmological solutions are reconstructed.
Exponential and power law solutions are reported for a well-known
$f(R,\mathcal{G})$ model, i.e., $f(R,\mathcal{G})=f_0R^n\mathcal{G}^{1-n}$.
Especially, the Kasner's solution is recovered and it is anticipated that the
familiar de-Sitter spacetime giving $\Lambda CDM$ cosmology may be
reconstructed for some suitable value of $n$.
