Answer to Question #218187 in Differential Equations for Efiii jaan

Question

Find complete integral of the equation
p+q=pq

Answer 1

Solution;

F(p,q)=p+q-pq=0

Let the complete integral of F(a,b) be given as;

In which p=a,q=b

z=ax+by+c.....(i)

Using our equation;

F(a,b)=a+b-ab=0

Solve for a;

a+b(1-a)=0

b=$\frac{a}{a-1}$

Which can be substituted back in the equation (i)

z=ax+$\frac{a}{a-1}$y+c

Answer;

z=$ax+\frac{a}{a-1}y+c$