query: Functional equation $f(xf(y)) = x^2y^a$
positive_passages.docid: 25953
positive_passages.text: Solving a functional relation $f\left( x \cdot f(y)\right)=x^2 \cdot y^a$
negative_passages.docid: 35281
negative_passages.text: $1992$ IMO Functional Equation problem
negative_passages.docid: 155806
negative_passages.text: (Olympiad Question) $f(2x) + 2f(y) = f(f(x+y))$
negative_passages.docid: 157744
negative_passages.text: Cauchy's functional equation with composite function: $gf(x+y)=gf(x)+gf(y)$
negative_passages.docid: 144859
negative_passages.text: Finding parameters for $f(x) = x^2 + 2(m − a)x + 3am −2 = 0$ that satisfy a condition.
negative_passages.docid: 79212
negative_passages.text: Find the general solution of $y'= a^{x + y}$ where y is the function
negative_passages.docid: 81921
negative_passages.text: If $f(x + y) = f(x) + f(y)$ showing that $f(cx) = cf(x)$ holds for rational $c$
negative_passages.docid: 125788
negative_passages.text: A function with a property $f(x+y)=f(x)f(y)$
negative_passages.docid: 128751
negative_passages.text: Solving for $f(2004)$ in a given functional equation
negative_passages.docid: 72769
negative_passages.text: How find this function $xf(x^2)=f(x),x>0$
negative_passages.docid: 44293
negative_passages.text: Functions satisfying $f\left( f(x)^2+f(y) \right)=xf(x)+y$
negative_passages.docid: 84318
negative_passages.text: A problem with the functional $F(\chi) = \int_{\mathbb{R}}(\chi'^2+\chi^2(1-\chi)^2)dx$.
negative_passages.docid: 131586
negative_passages.text: Hard functional equation: $ f \big ( x y + f ( x ) \big) = f \big( f ( x ) f ( y ) \big) + x $
negative_passages.docid: 104209
negative_passages.text: Functional equation - Cyclic Substitutions
negative_passages.docid: 55693
negative_passages.text: The functional equation $ f \big( x - f ( y ) \big) = f \big( f ( y ) \big) + x f ( y ) + f ( x ) - 1 $
negative_passages.docid: 28286
negative_passages.text: About finding the function such that $f(xy)=f(x)f(y)-f(x+y)+1$
negative_passages.docid: 13042
negative_passages.text: Finding a function from the given functional equation .