Differential algebraic equations

Differential equations, with combining algebraic conditions are lead to Differential Algebraic Equations (DAE). To solve them together cause various difficulties. In this discussion we give these difficulties and solutions. We include these algebraic variables to differential equation mostly and solve all unknowns? differential equations system. This differentiation work produce several difficulties in numerical solutions. Another problem is to give an initial condition coherent with new differential variables that join equation. In this discussion, we give first the definition of differential equation then structure of DAE and last some usefull numerical methods. There is no numerical method can solve every DAE. Most of problems have unique and spesific structures. Therefore, in this study we explain BDF (Backward Differential Formula) and make some numeric practises.