In this paper we have established the stability of a generalized nonlinear second-order differential equation in the sense of Hyers and Ulam. We also have proved the Hyers-Ulam stability of Emden-Fowler type equation with initial conditions.
 D. H. Hyers, “On the Stability of the Linear Functional Equation,” Proceedings of the National Academy of Sciences of the United States of America, Vol. 27, No. 4, 1941, pp. 222-224. doi:10.1073/pnas.27.4.222
 T. M. R assias, “On the Stability of the Linear Mapping in Banach Spaces,” Proceedings of the American Mathemaical Society, Vol. 72, No. 2, 1978, pp. 297-300. doi:10.1090/S0002-9939-1978-0507327-1
 T. Miura, S.-E. Takahasi and H. Choda, “On the Hyers- Ulam Stability of Real Continuous Function Valued Dif- ferentiable Map,” Tokyo Journal of Mathematics, Vol. 24, No. 2, 2001, pp. 467-476. doi:10.3836/tjm/1255958187
 S. M. Jung, “On the Hyers-Ulam-Rassias Stability of Approximately Additive Mappings,” Journal of Mathematics Analysis and Application, Vol. 204, No. 1, 1996, pp. 221-226. doi:10.1006/jmaa.1996.0433
 E. Takahasi, T. Miura and S. Miyajima, “On the HyersUlam Stability of the Banach Space-Valued Differential Equation ,” Bulletin of the Korean Mathematical Society, Vol. 39, No. 2, 2002, pp 309-315. doi:10.4134/BKMS.2002.39.2.309
 T. Miura, S. Miyajima and S.-E. Takahasi, “A Characterization of Hyers-Ulam Stability of First Order Linear Differential Operators,” Journal of Mathematics Analysis and Application, Vol. 286, No. 1, 2003, pp. 136-146.
 S. M. Jung, “Hyers-Ulam Stability of Linear Differential Equations of First Order,” Journal of Mathematics Analysis and Application, Vol. 311, No. 1, 2005, pp. 139-146. doi:10.1016/j.jmaa.2005.02.025
 G. Wang, M. Zhou and L. Sun, “Hyers-Ulam Stability of Linear Differential Equations of First Order,” Applied Mathematics Letters, Vol. 21, No. 10, 2008, pp 1024-1028. doi:10.1016/j.aml.2007.10.020
 Y. Li and Y. Shen, “Hyers-Ulam Stability of Nonhomogeneous Linear Differential Equations of Second Order,” International Journal of Mathematics and Mathematical Sciences, Vol. 2009, 2009, Article ID: 576852, p 7.
 P. Gavruta, S. Jung and Y. Li, “Hyers-Ulam Stability for Second-Order Linear Differential Equations With Boundary Conditions,” Electronic Journal of Differential Equations, Vol. 2011, No. 80, 2011, pp. 1-7.