Question

Functions satisfying $f\left( f(x)^2+f(y) \right)=xf(x)+y$

score 862 · Answer 1 · 2013-04-10 03:29:30

862

Views

Functions satisfying $f\left( f(x)^2+f(y) \right)=xf(x)+y$

Published on 10 Apr 2013 - 3:29

score 121 · Answer 2 · 2013-04-10 16:46:59

121

Views

Who can solve this ordinary differential equation?

Published on 10 Apr 2013 - 16:46

score 140 · Answer 3 · 2013-04-10 21:48:42

140

Views

If $h(x,c)$ is solution to equation $f'(x)=g(f(x))$, what is the solution for $-f'(x)=g(f(x))$?

Published on 10 Apr 2013 - 21:48

score 137 · Answer 4 · 2013-04-11 00:03:39

137

Views

Complex Constant and Convergent Power Series

Published on 11 Apr 2013 - 0:03

score 1.2k · Answer 5 · 2013-04-11 02:36:57

1.2k

Views

How to find all polynomials $P(x)$ such that $P(x^2+2x+3)=[P(x+3)]^2$?

Published on 11 Apr 2013 - 2:36

score 291 · Answer 6 · 2013-04-11 23:55:06

291

Views

Injectivity of a Function

Published on 11 Apr 2013 - 23:55

score 219 · Answer 7 · 2013-04-12 05:45:49

219

Views

Follow on from previous question: Functional Equation $f\big(f(x)^2+f(y)\big)=xf(x)+y$ - a little tricky

Published on 12 Apr 2013 - 5:45

score 2.5k · Answer 8 · 2013-04-12 06:01:44

2.5k

Views

Measurable Cauchy Function is Continuous

Published on 12 Apr 2013 - 6:01

score 189 · Answer 9 · 2013-04-12 09:12:56

189

Views

Is there a function $f$ such that $\Gamma (c+x)=\Gamma (c-f\left( x \right) )$?

Published on 12 Apr 2013 - 9:12

score 1.2k · Answer 10 · 2013-04-18 10:46:55

1.2k

Views

Find all differentiable functions $f$ such that $f\circ f=f$

Published on 18 Apr 2013 - 10:46

score 189 · Answer 11 · 2013-04-20 13:45:06

189

Views

Functional equation $(1-z)f(x)=f(\frac{1-z}{z}f(xz))$

Published on 20 Apr 2013 - 13:45

score 223 · Answer 12 · 2013-04-20 20:29:03

223

Views

A non-zero function satisfying $g(x+y)=g(x)g(y)$ must be exponential function

Published on 20 Apr 2013 - 20:29

score 4.2k · Answer 13 · 2013-04-21 15:26:52

4.2k

Views

Solving Differential Functional Equation $f(2x)=2f(x)f'(x)$

Published on 21 Apr 2013 - 15:26

score 9.9k · Answer 14 · 2013-04-21 18:09:51

9.9k

Views

Functional Equation $f(x+y)=f(x)+f(y)+f(x)f(y)$

Published on 21 Apr 2013 - 18:09

score 401 · Answer 15 · 2026-04-04 03:46:17

401

Views

Cauchy functional equation with non choice

Published on 04 Apr 2026 - 3:46

List Question

Functions satisfying $f\left( f(x)^2+f(y) \right)=xf(x)+y$

Who can solve this ordinary differential equation?

If $h(x,c)$ is solution to equation $f'(x)=g(f(x))$, what is the solution for $-f'(x)=g(f(x))$?

Complex Constant and Convergent Power Series

How to find all polynomials $P(x)$ such that $P(x^2+2x+3)=[P(x+3)]^2$?

Injectivity of a Function

Follow on from previous question: Functional Equation $f\big(f(x)^2+f(y)\big)=xf(x)+y$ - a little tricky

Measurable Cauchy Function is Continuous

Is there a function $f$ such that $\Gamma (c+x)=\Gamma (c-f\left( x \right) )$?

Find all differentiable functions $f$ such that $f\circ f=f$

Functional equation $(1-z)f(x)=f(\frac{1-z}{z}f(xz))$

A non-zero function satisfying $g(x+y)=g(x)g(y)$ must be exponential function

Solving Differential Functional Equation $f(2x)=2f(x)f'(x)$

Functional Equation $f(x+y)=f(x)+f(y)+f(x)f(y)$

Cauchy functional equation with non choice

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