Geometric Meaning of Differential Equations

Abstract

IN the Proceedings of the Royal Asiatic Society of Bengal, 1888, p. 76, Prof. Asutosh Mukhopadhyay has proposed a really excellent mode of geometric interpretation of differential equations in general: viz. writing the equation in form F = 0, the geometric meaning of the symbol F considered as a magnitude (angle, line, area, &c.), in any curve whatever (wherein F is of course not zero), is, if possible, to be formed; then the geometric meaning of that equation obviously is that the quantity F vanishes right round every curve of the family represented. This is the most direct geometrical interpretation yet proposed. Three examples have been given by him, all very neat. Writing for shortness the differential equations thus—