| Using a sample of 1.85 million DD¯ mesons collected at the Psi(3770) with the CLEO-c detector, and a reconstruction method based on the full event hermeticity, we measure branching fractions and branching fraction ratios for the four exclusive semileptonic decay modes D 0 → pi-e +nu, D0 → K -e+nu, D + → pi0e+nu and, D+ → K¯0 e+nu. For the branching fractions we find B (D0 → pi- e+nu) = 0.299 +/- 0.011 +/- 0.008%, B (D0 → K -e+nu) = 3.55 +/- 0.03 +/- 0.08%, B (D+ → pi0 e+nu) = 0.371 +/- 0.022 +/- 0.013% and B (D+ → K¯ 0e+nu) = 8.53 +/- 0.13 +/- 0.22%. The ratios are found to be B (D0 → pi- e+nu)/ B (D0 → K -e+nu) = 0.084 +/- 0.003 +/- 0.001, B (D+ → pi0 e+nu)/ B (D+ → K¯0 e+nu) = 0.044 +/- 0.003 +/- 0.001, Gamma( D0 → pi-e +nu)/Gamma(D+ → pi 0e+nu) = 2.04 +/- 0.14 +/- 0.08 and Gamma(D0 → K -e+nu)/Gamma(D + → K0e +nu) = 1.06 +/- 0.02 +/- 0.03. In addition, form factors are studied through fits to the partial branching fractions obtained in five q2 ranges. Combining our results with recent unquenched lattice calculations we extract the CKM matrix elements |Vcs | and |Vcd|. Averaging over isospin conjugate modes, we find |Vcs| = 1.01 +/- 0.01 +/- 0.01 +/- 0.11 and |Vcd| = 0.217 +/- 0.010 +/- 0.004 +/- 0.023. |
