MathDB
Problems
Contests
International Contests
Baltic Way
2015 Baltic Way
5
Functional Equation
Functional Equation
Source: Baltic Way 2015
November 8, 2015
algebra
functional equation
Baltic Way
Problem Statement
Find all functions
f
:
R
→
R
f:\mathbb{R}\to\mathbb{R}
f
:
R
→
R
satisfying the equation
∣
x
∣
f
(
y
)
+
y
f
(
x
)
=
f
(
x
y
)
+
f
(
x
2
)
+
f
(
f
(
y
)
)
|x|f(y)+yf(x)=f(xy)+f(x^2)+f(f(y))
∣
x
∣
f
(
y
)
+
y
f
(
x
)
=
f
(
x
y
)
+
f
(
x
2
)
+
f
(
f
(
y
))
for all real numbers
x
x
x
and
y
y
y
.
Back to Problems
View on AoPS