Magnetic flux surfaces allow us to examine surfaces in a laboratory environment. In this paper, we obtain differential equations to find the magnetic flux surfaces. Differential equations are needed for defining, modeling and solving engineering problems. They are particularly widely used in systems and control theory. First, we thought of linear combinations of Killing vector fields in three-dimensional Euclidean space E-3. We obtain partial differential equations by using these vectors. We find magnetic flux surface families with the solutions of these equations. Examples of the magnetic flux surface families members found by solving each equation are given.