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

ISBN-10: 1420010417

ISBN-13: 9781420010411

ISBN-10: 1584884762

ISBN-13: 9781584884767

"Featuring real-world purposes from engineering and technological know-how fields, A path in usual Differential Equations is the 1st booklet on usual differential equations (ODEs) to incorporate proper machine code and directions of MATLAB®, Mathematica®, and Maple. The ebook 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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that includes real-world functions from engineering and technological know-how fields, this publication on traditional differential equations (ODEs) comprises appropriate laptop code and directions of MATLAB[registered], Read more...

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Example text

Suppose that when a body is discovered at noon, its temperature is 82◦ F. Two hours later it is 72◦ F. If the temperature of the surroundings is 65◦ F, what was the approximate time of death? This problem is solved as the last example. Here T (0) represents the temperature when the body was discovered and T (2) is the temperature of the body 2 hours later. 8) becomes T (t) = 17ekt + 65. 3. PHYSICAL PROBLEMS WITH SEPARABLE EQNS so that T (t) = 17 7 17 37 t/2 + 65. This equation gives us the temperature of the body at any given time.

36. 37. 38. y 2 +2xy x2 dy 2x2 dx = x2 + dy dx = y2 xy − y = x2 + y 2 (x + 2y)dx − xdy = 0 (y 2 − 2xy)dx + x2 dy = 0 2x3 y = y(2x2 − y 2 ) (x2 + y 2 )y = 2xy xy − y = x tan( xy ) (2x + y)dx − (4x + 2y)dy = 0 y 2 + x2 y = xyy x − y + (y − x)y = 0 (x + 4y)y = 2x + 3y (x − y)dx + (x + y)dy = 0 ydx = (2x + y)dy y y = 2( x+y )2 39. 2xdy + (x2 y 4 + 1)ydx = 0 40. ydx + x(2xy + 1)dy = 0 41. A function F is called homogeneous of degree n if F (tx, ty) = tn F (x, y) for all x and y. That is, if tx and ty are substituted for x and y in F (x, y) and if tn is then factored out, we are left with F (x, y).

12. 13. 14. 15. 16. y 2 + 1dx = xydy √ (x2 − 1)y + 2xy 2 = 0, y( 2) = 1 y cot x + y = 2 y(0) = −1 y = 10x+y x dx dt + t = 1 y = cos(y − x) y − y = 2x − 3 (x + 2y)y = 1 y(0) = −2 √ y = 4x + 2y − 1 (y + 2) dx + y(x + 4) dy = 0, y(−3) = −1 8 cos2 y dx + csc2 x dy = 0, y(π/12) = π/4 17. dy dx = y 3 +2y x2 +3x , y(1) = 1 2 18. y = ex , y(0) = 0 2 19. y = xyex , y(0) = 1. Explain why this differential equation guarantees that its solution is symmetric about x = 0. 20. Find the solution of the equations that satisfies the given conditions for x → +∞: a.

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A course in ordinary differential equations by Stephen A. Wirkus, Visit Amazon's Randall J. Swift Page, search results, Learn about Author Central, Randall J. Swift,


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