The first ever investigation of the application of the Oslo Method in inverse kinematics experiments has been performed by analysis of an experiment where a 86Kr beam at 300 MeV was used on deuterated polyethylene/polystyrene targets at iThemba LABS to induce d(86Kr,p)87Kr reactions. The experiment was done at the AFRODITE array featuring two large volume (3.5x8") LaBr3(Ce) detectors, eight CLOVER detectors and two particle telescopes each consisting of two segmented silicon detectors. Problematic effects only seen in inverse kinematics such as Doppler shift, large angular dependencies, etc. have been solved. A new software code for analyzing inverse kinematics experiments with the Oslo Method was developed. The gamma-ray strength function and the level density of 87Kr was extracted and a large enhancement of the gamma-ray strength function at low energy was found. The experimental level density found was consistent with a constant temperature model for the level density.