Solution;
Given;
(px+y)2=px2
Let;
xy=v
Such that;
y+xdxdy=dxdv
Rewrite as;
y+xp=q
From which;
p=xq−y
By direct substitution into the equation;
(xq−y×x)+y)2=x2(xq−y)
Resolve to;
q2=xq−xy
q2=xq−v
Rewrite ;
v=xq−q2
Which is an equation of the form;
y=qx+f(p)
In which q=constant
Therefore;
v=cx−c2
But v=xy;
xy=xc−c2
Is the solution.
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