 Let us suppose that, in the equation M, N are homogeneous functions of x and y, of the same degree. In this case the fraction M/N is a function of y/x only, and we may write ?-/(*) (1) dx J \x) If we put y = xv this becomes 0) The variables x, v are now...  An Elementary Course of Infinitesimal Calculus - Page 471by Horace Lamb - 1897 - 616 pagesFull view - About this book
 | William Woolsey Johnson - Differential equations - 1883 - 44 pages
...of the First Order and Degree. 7. The equation Mdx + Ndy — 0 is said to be homogeneous when M and N are homogeneous functions of x and y of the same degree. Since the ratio of two homogeneous functions of the same degree is a function of — we may write the... | |
 | Mansfield Merriman, Robert Simpson Woodward - Mathematics - 1896 - 616 pages
...HOMOGENEOUS EQUATION. The differential equation Mdx + Ndy — o is said to be homogeneous when M and N are homogeneous functions of x and y of the same degree ; or, what is the same thing, when dy y -4- is expressible as a function of — . If in such an equation... | |
 | William Shaffer Hall - Calculus - 1897 - 280 pages
...DIFFERENTIAL EQUATIONS. The differential equation Mdx + Ndy = 0 is said to be homogeneous when M and N are homogeneous functions of x and y of the same degree. If the equation is written in the form dx=~N' y the second member is seen to be a function of -•... | |
 | John Perry - Calculus - 1897 - 398 pages
...h dv = 0, leading to * log x + — = c. X Solve (y - x) VlT^2 = n ( 1 + у")*. Cti37 239. If M and N are homogeneous functions of x and y of the same degree: assume y =vx and the equation reduces to the form of Art. 237. Example I. ydx + (2 -Jin/ - x) dy =... | |
 | William Anthony Granville - Calculus - 1904 - 490 pages
...Homogeneous equations. The differential equation Max + Ndy = 0 is said to be homogeneous when M and N are homogeneous functions of x and y of the same degree.* Such differential equations may be solved by making the substitution y=vx. This will give a differential... | |
 | University of Sydney - 1905 - 718 pages
...n'rst focus a point circle of the system. •6. Describe the method of solution of the equation where M, N are homogeneous functions of x and y of the same degree. Shew how to solve an equation of the form / ax+by+c \ ' \ a's + Vy + c'l What is a singular solution... | |
 | Alfred Lodge - Calculus, Integral - 1905 - 278 pages
...8. 9. 104. III. Homogeneous Equations. The equation Mdx + Ndy = 0 is called homogeneous when M and N are homogeneous functions of x and y of the same degree. If we introduce an auxiliary variable u such that y = ux, whence dy = udx + xdu, we shall be able to... | |
 | Edgar Jerome Townsend, George Alfred Goodenough - Calculus - 1908 - 522 pages
...integration from proper initial conditions. 159. Homogeneous equations. If in the equation M dx + N dy M and N are homogeneous functions of x and y of the same degree, the substitution y = vx reduces the equation to a form which permits separation of the variables. Ex.... | |
 | Frederick Shenstone Woods, Frederick Harold Bailey - Mathematics - 1909 - 446 pages
...equation . is readily solved. They are : 1. When the variables can be easily separated. 2. When M and N are homogeneous functions of x and y of the same degree. 3. When the equation is linear. 77. The equation Mdx + Ndy = 0 when the variables can be separated.... | |
 | Herman William March, Henry Charles Wolff - Calculus - 1917 - 386 pages
...Differential Equations. The differential equation M dx + N dy = 0 (1) is said to be homogeneous if M and N are homogeneous functions of x and y of the same degree. A function J(x, y) of the variables x and y is said to be homogeneous of degree n if after the substitutions... | |
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