math 251 quiz1 sample

# math 251 quiz1 sample - 2 + 1) sin y 2. If y = ( y-1) 3 (...

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Quiz 1(10 pts) Math 251, Fall 2011 NAME: THREE problems on two pages. SHOW YOUR WORK 1. Write down next to each equation if it is linear or nonlinear, autonomous or non au- tonomous, what is the order of the equation and if has the ﬁrst order if it is separable or not. Example: dy dt = sin ty 2 It is nonlinear,non autonomous, ﬁrst order, separable. 1. d 2 y dt 2 - d 3 y dt 3 = 2 y 2 + 5 2. dy dx = 2 xy + x 3 3. dy dt = ( t

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Unformatted text preview: 2 + 1) sin y 2. If y = ( y-1) 3 ( y-7) 5 ﬁnd the equilibrium solutions and ﬁnd asymptotic behavior of y ( t ) when t goes to inﬁnity, if y (10) = 5. Sketch this solution and the equilibrium solutions. 3. Solve: a. dy dx =-5 y-10 , y (0) = 4 b. dy dt =-y t-10 e t , Find the general solution. c. ( t 2-1) dy dt = yt-t, y (0) =-1...
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## This note was uploaded on 01/03/2012 for the course MATH 251 taught by Professor Chezhongyuan during the Fall '08 term at Penn State.

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math 251 quiz1 sample - 2 + 1) sin y 2. If y = ( y-1) 3 (...

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