Midterm1practice

# Midterm1practice - indicate on it the equilibrium solutions...

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NAME: Math 385 — Midterm 1 practice Total points: 100 . Please explain all answers. Calculators, computers, books and notes are not allowed. Suggestion: even if you cannot complete a problem, write out the part of the solution you know. You can get partial credit for it. 1. [20 points] Solve the following initial value problem for y = y ( x ): y 00 + 2 y 0 + 6 y = 0; y (0) = 0; y 0 (0) = 2 1

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NAME: 2. [20 points] Solve the following initial value problem for u = u ( t ): d 3 u dt 3 = - e t ; u (0) = 0; u 0 (0) = 0; u 00 (0) = 2 2
NAME: 3. [20 points] The evolution of the population P ( t ) is described by the equation dP/dt = P 2 - 5 P + 6. Sketch the corresponding slope ﬁeld and

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Unformatted text preview: indicate on it the equilibrium solutions and their stability. Consider then the population with initial condition P (0) = 4 and draw its evolution. What happens to this polulation as t increases? Verify your answer by calculating the exact solution for the given initial condition. 3 NAME: 4. [20 points] Solve the following initial value problem for x = x ( t ): dx dt + tx = te-t 2 / 2 ; x (0) =-1 4 NAME: 5. [20 points] Find the general solution of the following ODE for y = y ( x ): d 3 y dt 3-2 π d 2 y dt 2 + π 2 dy dt = 0 5...
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## This test prep was uploaded on 01/22/2011 for the course MATH 385 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

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Midterm1practice - indicate on it the equilibrium solutions...

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