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343_pdfsam_math 54 differential equation solutions odd

# 343_pdfsam_math 54 differential equation solutions odd -...

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Review Problems –1 –0.5 0 0.5 1 y –1 –0.5 0.5 1 x Figure 5–B : Integral curves and the direction field for Problem 15. 17. A trajectory is a path traced by an actual solution pair ( x ( t ) , y ( t )) as t increases; thus it is a directed (oriented) curve. An integral curve is the graph of a solution to the phase plane equation; it has no direction. All trajectories lie along (parts of) integral curves. A given integral curve can be the underlying point set for several different trajectories. 19. We apply Kirchhoff’s voltage law to Loops 1 and 2.
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Unformatted text preview: Loop 1 contains a capacitor C and a resistor R 2 ; note that the direction oF the loop is opposite to that oF I 2 . Thus we have q C − R 2 I 2 = 0 ⇒ q C = R 2 I 2 , where q denotes the charge oF the capacitor. Loop 2 consists oF an inductor L and two resistors R 1 and R 2 ; note that the loop direction is opposite to the direction oF I 3 . ThereFore, R 2 I 2 − R 1 I 3 − LI 3 = 0 ⇒ R 2 I 2 = R 1 I 3 + LI 3 . 339...
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