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" Homogeneous Exact Differentials. 131. Although the methods of integration just explained apply to all exact differentials, yet another and simpler process can be used when the expression belongs to the class called homogeneous. A differential expression... "
A Treatise on the Differential and Integral Calculus: And on the Calculus of ... - Page 365
by Edward Henry Courtenay - 1856 - 501 pages
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The Principles of Fluxions: Designed for the Use of Students in the Universities

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,...
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The Elements of the Integral Calculus: With Its Applications to Geometry and ...

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±£,...
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The Elements of the Integral Calculus: With Its Applications to Geometry and ...

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 +...
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A Treatise on the Differential and Integral Calculus: And on the Calculus of ...

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...
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A Treatise on the Differential and Integral Calculus: And on the Calculus 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....
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Elements of Analytical Geometry

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...
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Algebra for High Schools and Colleges: Containing a Systematic Exposition ...

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...
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A Treatise on the Differential and Integral Calculus: And on the Calculus of ...

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...
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A Treatise on the Differential and Integral Calculus: And on the Calculus of ...

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...
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Elements of Infinitesimal Calculus

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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