Differential Equations; a Short Course for Engineering Students
The book Differential Equations; a Short Course for Engineering Students was written by author James E James Ellsworth Boyd Here you can read free online of Differential Equations; a Short Course for Engineering Students book, rate and share your impressions in comments. If you don't know what to write, just answer the question: Why is Differential Equations; a Short Course for Engineering Students a good or bad book?
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Take the equation .(^y+y=o. (1) This may be written ^+4^=0. Differentiating, dividing by dy and solving the linear thus formed 1 iy^_1fdp_^ ,2) p^ p^ p^dy „dp . Zp-'i- __ 1 ,3, -P~^dy^ 2v 13;3"' * ' Substituting the value of /— 1 in (4) in equation (1) we get xy + 20/*+ Cy + l^O. (5) That (5) is the integral of (1) may be shown in the usual way by differentiating once and eliminating C. 1 dx In problems of this kind, instead of using — for—— to introduce 6 dv 26 EQUATIONS SOLVABLE FOR X. anothe...r new variable, the letter q is generally used in works on dif- dx ferential equations for——. The problem is then exactly the same as dy that of Art. 20, except that x and y change places. Using this nota- tion, equation ( 1 ) of the preceding paragraph becomes ;i:-|-V/=0. (1). Differentiating and dividing by dji 9 + 3?=y + 20/S ^ = 0. (2> ay From (3) we get the linear dq _,Zq _ _ J_ / 3 V dy ^ 2y 2y^' gy =y -\-C. ^'' Substituting (4) in (1) we get the same result as in the preceding case.
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