By Stephen A. Wirkus, Visit Amazon's Randall J. Swift Page, search results, Learn about Author Central, Randall J. Swift,
"Featuring real-world purposes from engineering and technology fields, A path in usual Differential Equations is the 1st publication on usual differential equations (ODEs) to incorporate appropriate desktop code and directions of MATLAB®, Mathematica®, and Maple. The booklet embeds the pc algebra code all through, providing the syntax subsequent to the proper concept. It totally describes approximations used to obtain numerical options. The authors additionally current reasons on the best way to use those courses to resolve ODEs and to qualitatively comprehend self reliant ODEs. With various appendices to complement studying, this booklet is perfect for college students and pros in arithmetic, engineering, and the sciences"--Publisher description. �Read more...
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Extra info for A course in ordinary differential equations
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). 2. SEPARABLE DIFFERENTIAL EQUATIONS 27 so that F is homogeneous of degree 2. Homogeneous diﬀerential equations and functions that are homogeneous of degree n are related in the following manner. Suppose the functions M and N in the diﬀerential equation M (x, y) dx + N (x, y) dy = 0 are both homogeneous of the same degree n.
13. A 20 L vessel contains air (assumed to be 80% nitrogen and 20% oxygen). 1 L of nitrogen is added to the container per second. If continual mixing takes place and material is withdrawn at the rate at which it is added, how long will it be before the container holds 99% nitrogen? 14. A 100-L beaker contains 10 kg of salt. Water is added at the constant rate of 5 L/min with complete mixing, and drawn oﬀ at the same rate. How much salt is in the beaker after 1 hour? 15. A tank contains 25 lb of salt dissolved in 50 gal of water.
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).
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,