{"id":"W2943969851","doi":"10.5539/jmr.v11n3p14","title":"On Liouvillian Solutions of Third Order Homogeneous Linear Differential Equations","year":2019,"lang":"en","type":"article","venue":"Journal of Mathematics Research","topic":"Coding theory and cryptography","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Homogeneous; Exponent; Invariant (physics); Combinatorics; Logarithm; Exponential function; Differential equation; Constant (computer programming); Mathematical physics; Pure mathematics; Mathematical analysis","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001100946,0.0009478899,0.000751373,0.001586294,0.00128002,0.001819165,0.001017201,0.0007839332,0.006820524],"category_scores_gemma":[0.00297025,0.0003209132,0.0009210606,0.001613672,0.00281026,0.002349081,0.002508055,0.002209919,0.001942677],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001577237,"about_ca_system_score_gemma":0.0008610085,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001945972,"about_ca_topic_score_gemma":0.00222464,"domain_scores_codex":[0.9994992,0.0001369201,0.00002687048,0.00006167608,0.0001623774,0.0001128103],"domain_scores_gemma":[0.999447,0.0002658239,0.0000810302,0.00005787262,0.00008805044,0.00006019109],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0001128277,0.00004883495,0.001041234,0.0001255723,0.00001391187,0.0003723526,0.001110929,0.008311908,0.003975172,0.9377739,0.00166302,0.04545037],"study_design_scores_gemma":[0.00006166956,0.0001210643,0.0005088671,0.0000717267,0.0000195736,0.000310425,0.0004755585,0.09202413,0.009884206,0.8738114,0.0226627,0.0000487651],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2168976,0.001359045,0.7058135,0.001125359,0.000302888,0.0001856354,0.0002213743,0.0006026505,0.07349197],"genre_scores_gemma":[0.6719105,0.001578289,0.2625727,0.0004441101,0.000229169,0.0001698874,0.0004438044,0.0003936398,0.06225787],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.006820524,"threshold_uncertainty_score":0.02281696,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.09084313278958654,"score_gpt":0.3563194632935208,"score_spread":0.2654763305039343,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}