Science:Math Exam Resources/Courses/MATH103/April 2009/Question 01 (c)

MATH103 April 2009

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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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If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

Hint
The steady state of a differential equation is a value for $\ y$, where ${\frac {dy}{dt}}=0$ for all $t\in \mathbb {R}$.

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Solution

Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. We need to check for which of these differential equations ${\frac {dy}{dt}}=f(y)$ 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 ${\frac {1}{3-3}}$ 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 ${\frac {dy}{dt}}=3$ which is never equal to 0 and has no steady state. So, the answer is (a).

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