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Phase Diagram - Differential Equations - Exam

Exams, Differential Equations

Post: March 31th, 2013
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Some keywords in Differential Equations are Convolution, Laplace Transform, Implicit Solution, Initial Condition, Integrating Factor, Autonomous Differential Equation, Appropriate Substitution. Some points of this exam paper are: Phase Diagram, Solve, Autonomous Differential Equation, Negative, Identify, Sketch Solution Curves, Equilibrium Solutions
Some keywords in Differential Equations are Convolution, Laplace Transform, Implicit Solution, Initial Condition, Integrating Factor, Autonomous Differential Equation, Appropriate Substitution. Some points of this exam paper are: Phase Diagram, Solve, Autonomous Differential Equation, Negative, Identify, Sketch Solution Curves, Equilibrium Solutions
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parvani
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Prof. S. Brick Spring ’06 Print your name: Differential Equations Exam 1 Math 238 section 101 Show all of your work, and explain your reasoning. 1. Solve y = xy 2 + x 2. Draw the phase diagram of the autonomous differential equation y = y (5 − y )(y + 2)2 and use it to sketch solution curves. (Here x ≥ 0, but y may be negative.) Identify and classify the types of equilibrium solutions. 3. The vertical motion of an object near the surface of the Earth is subject to two forces: a downward gravitational force FG = −mg (where m is the mass of the object, g is the gravitational constant, and the negative sign represents the downward direction) and a force FR due to air resistance. Assuming that the force due to air resistance is proportional to the velocity and using the fact that the sum of the forces is equal to the product of mass and acceleration, set up a differential equation for the velocity. Mention the signs of any other constants you use, explaining your reasoning..

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