In this paper, we compare two methods for solving Nonlinear Nonhomogeneous Volterra-Integral Equations with known exact algebraic solutions using the "Modified Decomposition Method" and demonstrate the existence and uniqueness of such solutions. Initially, using a numerical technique, a near-exact answer was quickly and easily obtained. Secondly, knowing that a solution to a multi-term Volterra equation always produces a partial combination of the input terms, a combinatory system was then used to find the correct combination representing the exact solution. This method grows exponentially and is only practical for a few terms Volterra equations. Both approaches are detailed with examples using Maple software with performance measurements that show that the numerical system is the winner if a near-exact solution is sufficient enough, which the case for most engineering applications is. For scientific and mathematical applications, the combinatory approach is preferred.

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