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The sum is Theorem 2 is another result of fundamental importance in many applications, for instance, in those methods for numerically determining eigenvalues and eigenvectors. We have three cases; this is similar to the situation for constant-coefficient equations, to which the Euler—Cauchy equation can be transformed Team Project 16 ; however, this fact is of theoretical rather than of practical interest. Systems of Units. The general solution of the homogeneous ODE dies out, practically after some short time theoretically never , and the transient solution goes over into a harmonic oscillation whose frequency is equal to that of the driving force or electromotive force. Comments on Content The student should become aware of the following facts: 1. To give the student a feel for the nature of ODEs and the general behavior of fields of solutions. F According to the hint given in the enunciation, the first step is to write the ODE 1 for y1 and then again for y2. The second normal mode looks similar to the portion of J0 between the second positive zero and the origin.