Transform the system (1) into a system of first order

Chapter 7, Problem 18

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Transform the system (1) into a system of first order equations by letting y1 = x1, y2 = x2,y3 = x1, and y4 = x2.Electric Circuits. The theory of electric circuits, such as that shown in Figure 7.1.2, consistingof inductors, resistors, and capacitors, is based on Kirchhoffs laws: (1) The net flow of currentinto each node (or junction) is zero, and (2) the net voltage drop around each closed loopis zero. In addition to Kirchhoffs laws, we also have the relation between the current I inamperes through each circuit element and the voltage drop V in volts across the element:V = RI, R = resistance in ohms;C dVdt = I, C = capacitance in farads1;LdIdt = V, L = inductance in henrys.Kirchhoffs laws and the currentvoltage relation for each circuit element provide a system ofalgebraic and differential equations from which the voltage and current throughout the circuitcan be determined. 19 through 21 illustrate the procedure just described.