| William Dealtry - Calculus - 1816 - 492 pages
...order ; and a similar 3C mode of definition may be used in the successive fluxions. (365.) An equation is said to be homogeneous, when the sum of the exponents of the variable quantities x and у is the same in each term ; as in the equation, axx + byx + djcy+cyy=0,... | |
| John Radford Young - Calculus, Integral - 1831 - 340 pages
...Differentials which are both Exact and Homogeneous. (80.) An algebraical function, consisting of several terms, is said to be homogeneous, when the sum of the exponents of the variables is the same in every term. Thus the following are homogeneous functions, viz. a*" fz + by *, ^-±^1 , m+J»l±£,... | |
| John Radford Young - Calculus, Integral - 1833 - 330 pages
...Differentials which are both Exact and Homogeneous. (80.) An algebraical function, consisting of several terms, is said to be homogeneous, when the sum of the exponents of the variables is the same in every term. Thus the following are homogeneous functions, viz. ax^y3 + i/6 axy + if + z2 ax3 if z +... | |
| Edward Henry Courtenay - Calculus - 1855 - 526 pages
...SRdz =fzdz = ~ z2. . •. « = (x2 + y2 + z2) + tan- + y' + z2 + C. Homogeneous Exact Differential*. 131. Although the methods of integration just explained...is the same in the coefficient of every term. Thus ax^dx xdy + ydx, x2zdx + xzzdx — xyzdy, and — — are homogeneous differentials. The degree of... | |
| Edward Henry Courtenay - Calculus - 1857 - 522 pages
...we get , and finally taking the terms in R which do not contain x nor y, i- + 5^ + \z2 + C. IS o * Homogeneous Exact Differentials. 131. Although the...is the same in the coefficient of every term. Thus ax2dx — ly"Jy xdy + ydx, x*zdx + xz'dx — xyzdy, and — — y — ^jj7> are homogeneous differentials.... | |
| Albert Ensign Church - Geometry, Analytic - 1859 - 360 pages
...cylinder. CHAPTER XIII. Oa the Integration of Homogeneous and Linear Differentials. (Art. 111.) An equation is said to be homogeneous when the sum of the exponents of the variables is the same in every term. Differentials of this form can always be integrated. In such cases we place one of the... | |
| James B. Dodd - Algebra - 1859 - 368 pages
...according to which the polynomial is arranged, is called the letter of arrangement. (23.) A polynomial is said to be homogeneous, when the sum of the exponents of the literal factors, is the same in each of its terms. ' Thus a3 -\-2ax2 — bey is homogeneous, since... | |
| Edward Henry Courtenay - Calculus - 1873 - 524 pages
...г, we get /Afe =/2<fe = z». , and finally taking the terms in R which do not contain x nor y, (7. Homogeneous Exact Differentials. 131. Although the...the coefficient of every term. Thus xdy + ydx, xzzdx + ат22Чг — xyzdy, and a are homogeneous differentials. The degree of the terms is estimated by... | |
| Edward Henry Courtenay - Calculus - 1873 - 528 pages
...get and finally taking the terms in R which do not contain x nor y, /Afc <./«*e* tan-i- + \ Sí o Homogeneous Exact Differentials. 131. Although the...in the coefficient of every term. Thus xdy -\- ydx, x2zdx + xzWx — xyzdy, and -äy are homogeneous differentials. The degree of the terms is estimated... | |
| Joseph Bayma - Calculus - 1889 - 296 pages
...1 x or x 83. When the equation Mdx + Kdy = 0 is homogeneous with regard to the variables, that is, when the sum of the exponents of the variables is the same in M as in N, the variables c;m be separated by the aid of an auxiliary variable. Let tfdy — y (x -\-... | |
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