164 MATHEMATICAL FORMULAE AND ELLIPTIC FUNCTIONS 



8.033 An equation of the form, 



has an integrating factor: 



xP-yQ 



8.034 If 



dP _ dQ 



dy_d? m F(x) 



is a function of x only, an integrating factor is 



8.035 If 



is a function of y only, an integrating factor is 



e fF(y)dy t 



8.036 If 



dP_ dQ 



= F , ) 



Qy - Px 

 is a function of the product xy only, an integrating factor is 



e fF(xy)d(xy) ^ 



8.037 Jf 



dx dy (y 

 Px + Qy * U 



is a function of the quotient - only, an integrating factor is 



8.040 Ordinary differential equations of the first order and of degree higher 

 than the first. 



Write: 



dy_ p 



General form of equation: 



/(*, y, P) = o. 



