Abstract: The telegraph equation is often used to analyze the electromagnetic transients on transmission lines. The paper discusses the analytical solution to the equation with difficult boundary conditions that the line is excited by a step voltage source at one end and is open-circuited at the other end. The resistance of the line is taken into account. Two methods are employed. The method of separation of variables is used to solve the partial differential equation,and residues are calculated to conduct invers Laplace transform. The analytical solution is in the form of a trigonometric series. Each of its harmonic components is a standing wave,which can be converted into the familiar superposition of a forward and a backward traveling waves. Though the two methods follow completely different technical routes,they result in exactly the same formula.