Using 2.93 fb-1 of data taken at 3.773 GeV with the BESIII detector operated at the BEPCII collider, we study the semileptonic decays D+→K̄0e+νe and D+→π0e+νe. We measure the absolute decay branching fractions B(D+→K̄0e+νe)=(8.60±0.06±0.15)×10-2 and B(D+→π0e+νe)=(3.63±0.08±0.05)×10-3, where the first uncertainties are statistical and the second systematic. We also measure the differential decay rates and study the form factors of these two decays. With the values of |Vcs| and |Vcd| from Particle Data Group fits assuming Cabibbo-Kobayashi-Maskawa (CKM) unitarity, we obtain the values of the form factors at q2=0, f+K(0)=0.725±0.004±0.012, and f+π(0)=0.622±0.012±0.003. Taking input from recent lattice QCD calculations of these form factors, we determine values of the CKM matrix elements |Vcs|=0.944±0.005±0.015±0.024 and |Vcd|=0.210±0.004±0.001±0.009, where the third uncertainties are theoretical.