Draw the phase portraits of the following systems, using isoclines(a)Ö+0+0.50=0(b)+0+0.50 = 1(c)+8² +0.50=0

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Answered: Draw the phase portraits of the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Example 4 (Calculator Active): For 0 ≤s ≤ 5000, the total amount a local college spends on printing is related to the number of students enrolled at the school and is modeled by C(s) = 70-32 cos (2000) where s is the number of students enrolled at the college and C is the total cost of printing, in thousands of dollars. At what rate is the total cost of printing changing, in dollars per student, when 2500 students are enrolled at the college?
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Suppose you are going to graph the function f(x) =-3 cot (3x + c), where cis an unknown constant. If the graph includes a phase shift of 2 units to the right, find the value of c.
Suppose that we have a mass-spring system that follows the simple harmonic motion described by the equation s= 6cos(pi t) , where s represents displacement measured in centimeters and time is measured in seconds. The maximum displacement of the mass is ___cm. The system's frequency is ____cycles per second. The displacement of the mass after 3/2 second is____ The first time where the mass passes through the equilibrium point is _____ .
1 A tank contains 480 gallons of water and 15 oz of salt. Water containing a salt concentration of (1 + sint) oz/gal flows into the tank 2 at a rate of 5 gal/min, and the mixture in the tank flows out at the same rate. The long-time behavior of the solution is an oscillation about a certain constant level. What is this level? What is the amplitude of the oscillation? Round the values to two decimal places. Oscillation about a level = i Amplitude of the oscillation = OZ. OZ.
What is the amplitude and phase shift of the equation u(t)=0.2cos3t+0.3sin3t? A = A = A=- 13 10 13 10 13 10 13 10 ; 8= -0.98 ; 8=0.98 ; 8=-0.59 ; 8=0.59
2a. Find a change of variable that transforms the equation into an autonomous equation change of variable: new equation: b. Sketch the phase line for the resulting equation and use it to sketch graphs of the long-term behaviors of all the qualitatively different solutions for the new variable, and then for the original equation.
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Draw the phase portraits of the following systems, using isoclines (a) +0+0.50=0