Question

Can any body explain how to solve this partial diff. eqn.:

(y-x)(qy-px)=(p-q)^2


where p and q have there usual meaning

Answer 1

Use the substitution X=x+y and Y=xy which reduces the given equation to P=\[Q^{2}\]. Then use Charpit's Method to get P=a and Q=\[\sqrt{a}\]. Which gives you z=a(x=y)+\[\sqrt{a}\]xy+b