VIII. DIFFERENTIAL EQUATIONS. 



8.000 Ordinary differential equations of the first order. General form: 



8.001 Variables are separable. f(x, y) is of, or can be reduced to, the form; 



where X, is a function of x alone and Y is a function of y alone. 

 The solution is: 



fxdx + fdy = C. 

 / */ 



8.002 Linear equations of the form: 



-2- + P(x)y = Q(x)~. 

 Solution : 



y = e ~fP^ 



8.003 Equations of the form: 



f x +p(x) y = 



Solution : 



yn-l 6 l ) J VW e 



^8.010 Homogeneous equations of the form: 



dy P(ag, 



where P(#, y) and Q(x, y) are homogeneous functions of x and y of the same 

 degree. The change of variable: 



y = vx, 

 gives the solution: 



