 | Edward Henry Courtenay - Calculus - 1855 - 526 pages
...when the equation can be reduced to the form Xdx + Tdy = 0, where X is a function of x only, and T a function of y only. The form of the solution will then be The separation of the variables is possible in several cases. 140. Case 1st. Let the form be Ydx +... | |
 | Edward Henry Courtenay - Mathematics - 1856 - 524 pages
...the equation can be reduced to the form Xdx + YJy = 0, i who.re X is a function of x only, and Y & function of y only. The form of the solution will then be Ib + w= C, which requires only the integration of functions of a single variable. The separation of... | |
 | Edward Henry Courtenay - Calculus - 1868 - 530 pages
...the variables is possible, that is, when the equation can bo reduced to the form Xdx + Ydy = 0, where X is a function of x only, and Y a function of y only. The form of the solution will then be Fx + ipy = C, which requires only the integration of functions of a single variable• The separation... | |
 | Mathematics - 1901 - 476 pages
...the resulting row is d(a, a), 0, 0. Hence we take о = ß = a, s = Ь, z = Ьху + X + Y, X being a function of x only and Y a function of y only. Then а = a is a relation connecting x, d~K/dx, c22X/Wic2, and ß = a is a relation connecting y, dY/dy,... | |
 | Ovid Wallace Eshbach, Byron D. Tapley - Technology & Engineering - 1990 - 2104 pages
...given to Laplace's equation V2" = —^ + —^ = 0 (2.342) ox ay Assume that u= X(x)- Y(y) (2.343) where X is a function of x only, and Y a function of y only. By substitution and dividing by X • Y, (2.342) becomes 1 d2X 1 d2Y -X^'—Y^ (2'344) Since the left... | |
 | Derek Richards - Computers - 2002 - 884 pages
...the membrane is rectangular it is sensible to assume a solution of the form F(r) = X(x)Y(y), where X is a function of x only and Y a function of y only. On substituting this into the above equation and dividing by F we arrive at the equation ^d2^ ^d2^... | |
 | Bansi Lal - 2006 - 414 pages
...separable. Rule to solve an equation in which the variables dy are separable, ie, 3— = XY, where X is a function of x only and Y a function of y dx only: (¿) Multiply thro' out by dx. (ii) Separate the variables x and y (ie, get all the functions... | |
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C, where C is an arbitrary constant. 139. Again, the integration can be effected whenever the separation of the variables is possible, that is, when the equation can be reduced to the form Xdx + Tdy = 0, whore X is a function of x only, and Y a function... 