In order to efficiently provide demand side management (DSM) in smart grid, carrying out pricing on the basis of real-time energy usage is considered to be the most vital tool because it is directly linked with the finances associated with smart meters. Hence, every smart meter user wants to pay the minimum possible amount along with getting maximum benefits. In this context, usage based dynamic pricing strategies of DSM plays their role and provide users with specific incentives that help shaping their load curve according to the forecasted load. However, these reported real-time values can leak privacy of smart meter users, which can lead to serious consequences such as spying, etc. Moreover, most dynamic pricing algorithms charge all users equally irrespective of their contribution in causing peak factor. Therefore, in this paper, we propose a modified usage based dynamic pricing mechanism that only charges the users responsible for causing peak factor. We further integrate the concept of differential privacy to protect the privacy of real-time smart metering data. To calculate accurate billing, we also propose a noise adjustment method. Finally, we propose Demand Response enhancing Differential Pricing (DRDP) strategy that effectively enhances demand response along with providing dynamic pricing to smart meter users. We also carry out theoretical analysis for differential privacy guarantees and for cooperative state probability to analyze behavior of cooperative smart meters. The performance evaluation of DRDP strategy at various privacy parameters show that the proposed strategy outperforms previous mechanisms in terms of dynamic pricing and privacy preservation.