  The tagged quasi-free $np \to np\pi^+\pi^-$ reaction has been studied
experimentally with the High Acceptance Di-Electron Spectrometer (HADES) at GSI
at a deuteron incident beam energy of 1.25 GeV/nucleon ($\sqrt s \sim$ 2.42
GeV/c for the quasi-free collision). For the first time, differential
distributions for $\pi^{+}\pi^{-}$ production in $np$ collisions have been
collected in the region corresponding to the large transverse momenta of the
secondary particles. The invariant mass and angular distributions for the
$np\rightarrow np\pi^{+}\pi^{-}$ reaction are compared with different models.
This comparison confirms the dominance of the $t$-channel with $\Delta\Delta$
contribution. It also validates the changes previously introduced in the
Valencia model to describe two-pion production data in other isospin channels,
although some deviations are observed, especially for the $\pi^{+}\pi^{-}$
invariant mass spectrum. The extracted total cross section is also in much
better agreement with this model. Our new measurement puts useful constraints
for the existence of the conjectured dibaryon resonance at mass M$\sim$ 2.38
GeV and with width $\Gamma\sim$ 70 MeV.
