Abstract    In this paper we suggest a method to calculate the first integrals of a special system of the first order of differential equations. Then we use the method for finding the solutions of some differential equations such as, the differential equation of RLC circuit.

Keywords    Distribution, First Integral, RLC Circuit, Heat Capacity

References    1. Giordano, F. R. and Weir, M. D., “Differential Equations: A Modeling Approach”, Addison-Wesley, Reading Ma, U.S.A., (1994). 2. Ibragimov, N. H., “Group Analysis of Ordinary Differential Equations and the Invariance Principle in Mathematical Physics (for the 150th anniversary of Sophus Lie)”, Russian Math., Vol. 47, No. 4, (1992), 89-156. 3. Kushner, A., Lychagin, V. and Rubstov, V., “Contact Geometry and Non-Linear Differential Equations”, Cambridge University Press, Cambridge, U.K., (2007). 4. Lee, J. M., “Introduction to Smooth Manifolds”, Springer Verlage, New York, U.S.A., (2002). 5. Olver, P. J., “Applications of Lie Groups to Differential Equations, Second Edition”, GTM, Springer Verlage, New York, U.S.A., Vol. 107, (1993). 6. Olver, P. J., “Equivalence Invariants and Symmetry”, Cambridge University Press, Cambridge, U.K., (1995). 7. Sharpe, R. W., “Differential Geometry: Cartan Generalization of Klein's Erlangen Program”, GTM, Springer Verlage, New York, U.S.A., Vol. 166, (1996).