We consider the differential equations associated with newly discovered orthogonal polynomials, namely the exceptional Xm Laguerre and Xm Jacobi orthogonal polynomials, and discuss their solutions explicitly. These polynomials are the combination of corresponding classical orthogonal polynomials. In contrast to the classical polynomials, the properties associated with these exceptional polynomials are completely different. As an illustration, we consider the X1 and X2 cases and show the behaviors of these functions graphically. Further, we compare these results with the corresponding classical polynomials.