Question

The complete integral of p+q = pq is given by


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Answer 1

Answer:

The complete integral of p + q = pq is given by z=ax+( a a−1 )y+c …(5) Page 14 105 Differentiating (5) partially w.r.t c, we get 0 = 1, which is absurd. Hence, singular integral does not exist.

Answer 2

The complete integral of p+q = pq is $px+\frac{p}{p-1} y +c$.

Step 1:Find complete integral.

Given:- p+q =pq

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 = $ax+\frac{a}{a-1} y +c$  

putting back a=p

z = $px+\frac{p}{p-1} y +c$