This paper introduces analytical and numerical solutions of the nonlinear Langevin’s equation under square nonlinearity with stochastic non-homogeneity. The solution is obtained by using the Wiener-Hermite expansion with perturbation (WHEP) technique, and the results are compared with those of Picard iterations and the homotopy perturbation method (HPM). The WHEP technique is used to obtain up to fourth order approximation for different number of corrections. The mean and variance of the solution are obtained and compared among the different methods, and some parametric studies are done by using Matlab.
 B. A. Georges, “Random Generalized Solutions to the Heat Equations,” Journal of Mathematical Analysis and Applications, Vol. 60, No. 1, 1977, pp. 93-102. http://dx.doi.org/10.1016/0022-247X(77)90051-8
 W. T. Coffey and Y. P Kalmykov, “The Langevin Equation, with Applications to Stochastic Problems in Physics, Chemistry and Electrical Engineering,” 3rd Edition, World Scientific Publishing Company, Singapore City, 2012.
 M. A. El-Beltagy and M. A. El-Tawil, “Toward a Solution of a Class of Non-Linear Stochastic perturbed PDEs Using Automated WHEP Algorithm,” Applied Mathematical Modelling, 2013, in Press. http://dx.doi.org/10.1016/j.apm.2013.01.038
 M. El Tawil and W. Shawky “Wiener Functional, Integrals, and Stochastic Differential Equations Solutions Using EulerMaruyama, Picard and WHEP Computer Simulation Stud,” BSc Thesis, Engineering faculty, Cairo University, Cairo, 2011.
 M. A. El-Tawil and A. Fareed, “Solution of Stochastic Cubic and Quintic Nonlinear Diffusion Equation Using WHEP, Pickard and HPM Methods,” Open Journal of Discrete Mathematics, Vol. 1, No. 1, 2011, pp. 6-21.
 M. El-Tawil and N. El-Molla, “The Approximate Solution of a Nonlinear Diffusion Equation Using Some Techniques, a Comparison Study,” Applied Mathematics and Computing, Vol. 29, No. 1-2, 2009, pp. 281-299.
 A. S. El-Johani, “Comparisons between WHEP and Homotopy Perturbation Techniques in Solving Stochastic Cubic Oscillatory Problems,” AIP Conference Proceedings, Vol. 1148, 2010, pp. 743-752. http://dx.doi.org/10.1063/1.3225426
 J. C. Cortes, J. V. Romero, M. D. Rosello and R. J. Villanueva, “Applying the Wiener-Hermite Random Technique to Study the Evolution of Excess Weight Population in the Region of Valencia (Spain),” American Journal of Computational Mathematics, Vol. 2, No. 4, 2012, pp. 274-281. http://dx.doi.org/10.4236/ajcm.2012.24037
 R. H. Cameron and W. T. Martin, “The Orthogonal Development of Non-Linear Functionals in Series of Fourier-Hermite Functionals,” Annals of Mathematics, Vol. 48, No. 2, 1947, pp. 385-392.
 T. Imamura, W. Meecham and A. Siegel, “Symbolic Calculus of the Wiener Process and Wiener-Hermite Functionals,” Journal of Mathematical Physics, Vol. 6, No. 5, 1965, pp. 695-706.
 W. C. Meecham and D. T. Jeng, “Use of the Wiener-Hermite Expansion for Nearly Normal Turbulence,” Journal of Fluid Mechanics, Vol. 32, No. 2, 1968, pp. 225-235.
 E. A. Ibijola and B. J. Adegboyegun, “A Comparison of Adomian’s Decomposition Method and Picard Iterations Method in Solving Nonlinear Differential Equations,” Nigeria Global Journal of Science Frontier Research Mathematics and Decision Sciences, Vol. 12, No. 7, 2012.
 I. K. Youssef, “Picard Iteration Algorithm Combined with Gauss-Seidel Technique for Initial Value Problems,” Applied Mathematics and Computation, Vol. 190, No. 1, 2007, pp. 345-355. http://dx.doi.org/10.1016/j.amc.2007.01.058
 J. H. He, “Application of Homotopy Perturbation Method to Nonlinear Wave Equations,” Chaos Solitons Fractals, Vol. 26, No. 3, 2005, pp. 295-300. http://dx.doi.org/10.1016/j.chaos.2005.03.006