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 = 2y6 (b) dy/dt = y^{2}+9 (c) dy/dt = 1/(3y) (d) dy/dt = cos(πy) (e) dy/dt = 3 
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Hint 

The steady state of a differential equation is a value for , where
for all . 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. 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 3^{2}+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). 