<p>One of a powerful application in the age of cloud computing is the outsourcing of scientific computations to cloud computing which makes cloud computing a very powerful computing paradigm, where the customers with limited computing resource and storage devices can outsource the sophisticated computation workloads into powerful service providers. One of scientific computations problem is Two-Point Boundary Value Problems(BVP) is a basic engineering and scientific problem, which has application in various domains. In this paper, we propose a privacy-preserving, verifiable and efficient algorithm for Two-Point Boundary Value Problems in outsourcing paradigm. We implement the proposed schema on the customer side laptop and using AWS compute domain elastic compute cloud (EC2) for the cloud side.</p>