Any electric circuit is governed by the law of electric circuits: Kirchhoff's voltage and current laws, Ohm's law, and the other laws of capacitor and inductor. To know the behavior of electric circuit is exactly same as to solve a simultaneous equation consisting of the laws of electric circuit. Students learn how to solve it effectively by hand.
More electric elements and nodes in the circuit lead to the number of equations to be solved. Since real circuits have many elements and are complicated, and often very difficult to solve by hand, numerical simulation is used to know how the circuit behaves as time goes. In fact, so-called SPICE is de facto standard in the industry. You can see how every voltage and current in your circuit changes in time, if you give concrete values to all elements to the simulator software. However, if you have to decide parameters of some elements to have a better circuit, you would perform simulations with different parameters, and then choose one best set of parameters to meet your requirement. Even if you reach the best, you can never say that this is the best, because it is the best among your trial. Thus the true best may be outside of your trial.
Symbolic computation of electric circuits will be able to find the best parameters. It is, however, true only if the computation is finished in a realistic time period. The method to obtain a single state-space equation with the laws of circuits has been deeply studied in the literature mainly in 1950's. Now we have much faster and more powerful computation environment than those days. Thus we should revisit classical results on electric circuit and revise them to modern computation algorithm, and evaluate them with a realistic amount of computation.