Science:Math Exam Resources/Courses/MATH103/April 2009/Question 01 (c)
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Question 01 (c)
Multiple Choice question: Select ONE correct answer. You will not be graded for any work.
For which of these differential equations is y = 3 a steady state solution?
(a) dy/dt = 2y-6
(b) dy/dt = y2+9
(c) dy/dt = 1/(3-y)
(d) dy/dt = cos(πy)
(e) dy/dt = 3
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The steady state of a differential equation is a value for , where
for all .
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We need to check for which of these differential equations it holds that f(3) = 0.
For the first one we see that 2(3) - 6 = 0. So, y=3 is a steady state.
For the second equation we have 32+9=18 ≠ 0. So, y=3 is no steady state.
The third equation is not even defined for y=3.
For the forth equation we have cos(π 3) ≤ 0, and y=3 is no steady state.
Last we have the differential equation which is never equal to 0 and has no steady state.
So, the answer is (a).