Higher Mathematics; A Text-Book for Classical and Engineering Colleges
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Higher Mathematics; A Text-Book for Classical and Engineering Colleges

Higher Mathematics; A Text-Book for Classical and Engineering Colleges


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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1902 Excerpt: ...in question is shared by all the members of a system of similar curves. The solution of a question of this nature will thus in general be a system of curves, the complete integral of a differential equation, but it may be a singular solution. Thus, if we express the property that the sum of the intercepts on the axes made by the tangent to a curve is equal to the constant a, the straight lines making such intercepts will themselves constitute the complete integral system, and the curve required is the singular solution, which, in accordance with Art. 8, is the envelope of these lines. The result in this case will be found to be the parabola Vx-Vy = Va. An important application is the determination of the "orthogonal trajectories" of a given system of curves, that is to say, the curves which cut at right angles everycurve of the given system. The differential equation of the trajectory is readily derived from that of the given system; for at every point of the trajectory the value of p is the negative reciprocal of its value in the given differential equation. We have therefore only to substitute--/"' for p to obtain the differential equation of the trajectory. For example, let it be required to determine the orthogonal trajectories of the system of parabolas y = A, ax having a common axis and vertex. The differential equation of the system found by eliminating a is 2 xdy = y dx. dx dv Putting in place of---, the differential equation of dy dx the system of trajectories is 2xdx--ydy = o, whence, integrating, 2x+/ = (. The trajectories are therefore a system of similar ellipses with axes coinciding with the coordinate axes. Prob. 46. Show that when the differential equation of a system is of the second degree, its discriminant and that of its tr...


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Product Details
  • ISBN-13: 9781236135872
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 142
  • Spine Width: 8 mm
  • Width: 189 mm
  • ISBN-10: 1236135873
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 268 gr


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