Modern instruments and methods of calculation : a handbook of the Napier Tercentenary Exhibition (1914)
Horsburg, E. M. (Ellice Martin), Napier Tercentenary Exhibition (1914 : Edinburgh, Scotalnd) · London : G. Bell · leaf 213
g differential equation solved is r>_ Q{x)-y±am {] y aTm(Q(x)~y) W) Integraph for a Canonical Form of Riccatis Equation § 3. B and E are fixed pivots on AB for two grooved bars BSA and ES. The point S moves on these so that ES and IA are parallel, and theintegrating wheel at I is directed along… … Fig. 3. Since BTBE=BA/BS=«A and IS is the line .-. Bl=ab/\, y=x(m—ab/X2) -\-abjX. (8) Its gradient is .-. m- -ab/X *=m- -Biy ab. Hence we obtain the differential equat ion . 1 y = m —yi lab a y* ab or (9) aby-\-y*=bQ{x) This is a canonical form of the equation of Riccati y=Aya+By+C, (10) in which…
