The substitution of the infinite series in the partial differential equations (PDEs) and boundary conditions results in an infinite system of ordinary differential equations with appropriate boundary conditions which must be solved analytically or otherwise. In this chapter, the authors sum up the series solution. The convergence of the series may be proved numerically or analytically. The authors take up several problems for which closed form exact solutions are known for some special cases, say for plane geometry. These special exact solutions motivate infinite series form of the solution for the more general problems. The approach is best understood by discussing the solution of some specific problems taken mostly from gasdynamics. The gas-vacuum interface is related, in a sense, to an infinitely strong shock. The gas-vacuum front, in short, behaves in certain respects like an infinitely strong shock.