# A course in ordinary differential equations by Stephen A. Wirkus, Visit Amazon's Randall J. Swift Page,

By Stephen A. Wirkus, Visit Amazon's Randall J. Swift Page, search results, Learn about Author Central, Randall J. Swift,

"Featuring real-world functions from engineering and technology fields, A direction in traditional Differential Equations is the 1st booklet on traditional differential equations (ODEs) to incorporate suitable desktop code and directions of MATLAB®, Mathematica®, and Maple. The publication embeds the pc algebra code all through, offering the syntax subsequent to the appropriate idea. It absolutely describes approximations used to obtain�Read more...

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**Example text**

0 sec before falling. Neglecting air resistance, with what velocity was the ball thrown? 5. 00 sec before it hits the ground. If air resistance is neglected, answer the following questions: a. What was its ﬁnal velocity just as it hit the ground? b. What was the average velocity during the fall? c. How high was the building? 6. 00 sec later you see it hit the ground. Neglecting air resistance, how high is the cliﬀ? 7. Superman is ﬂying at treetop level near Paris when he sees the Eiﬀel Tower elevator start to fall (the cable snapped).

2 Using the condition that the object fell from rest, so that v(0) = 0, we can determine the constant c and solve for v(t). We have v(t) = 4 − 4e−8t as the velocity of the object at any time. 3. 3 shows the behavior of the velocity over time. Analytically, we see that v(t) approaches 4 as t → ∞. This value is known as the limiting or terminal velocity of the object. Now since dx dt = v(t), we have dx = 4 − 4e−8t . dt This is easily integrated to obtain x(t) = 4t + 12 e−8t + c. If we take the initial position of the object as zero, so that x(0) = 0, then 1 1 x(t) = 4t + e−8t − .

1. SOME BASIC TERMINOLOGY 9 18. Find values of r for which y(x) = xerx is a solution to y + 4y + 4y = 0 on (−∞, ∞). 19. Classify the diﬀerential equations by specifying (i) the order, (ii) whether it is linear or nonlinear, and (iii) whether it is an initial-value or boundaryvalue problem (where appropriate). a. 3y + y = sin x b. y + sin y = 0 c. y (3) + (sin x)y (2) + y = x, y(0) = 1, y (0) = 0, y (0) = 2 d. y + ex y = y 4 , y(0) = 0 e. y + y − y = 0 f. y + ex y + y 2 = 0, y(0) = 1, y(π) = 0 20.