5x2 5y 45 E O

2.3 Integral curves of y = ( y cos x )/(1 + 2 y 2 ). The investigation of a first order nonlinear equation can sometimes be facilitated by regarding both x and y as functions of a third variable t . Then dy /dt dy = . dx dx /dt (26) 45 2.2 Separable Equations If the differential equation is dy F (x , y ) = , dx G (x , y ) (27) then, by comparing numerators and denominators in Eqs. (26) and (27), we obtain the system dx /dt = G (x , y ), dy /dt = F (x , y ).