If $x'(t) \leq f(x(t))$, then $x(t)\leq y(t)$ for which $y'(t)=f(y(t))$?
8145
Comparison theorem for ODE
111186
Proving that if $|f''(x)| \le A$ then $|f'(x)| \le A/2$
122944
Prove $|y''(x)| \leq 40$ for all $x \in [1,3]$.
134880
Is there a difference between $y(x)$ and $f(x)$
1626
How do we prove $\int_I\int_x^1\frac{1}{t}f(t)\text{ dt}\text{ dx}=\int_If(x)\text{ dx}$
74583
Prove that $f'(0)=L$.
48592
Prove that $f'$ exists for all $x$ in $R$ if $f(x+y)=f(x)f(y)$ and $f'(0)$ exists
21891
If $f(xy)=f(x)f(y)$ then show that $f(x) = x^t$ for some t
48275
$f$ defined $|f(x) - f(y)| \leq |x - y|^{1+ \alpha}$ Prove that $f$ is a constant.
64339
Find $f$ where $f'(x) = f(1+x)$
99917
What function satisfies $F'(x) = F(2x)$?
77133
$g'(x) = \frac{1}{x}$ for all $x > 0$ and $g(1) = 0$. Prove that $g(xy) = g(x) + g(y)$ for all $x, y > 0$.
145424
If $f''(x)+f(x)>0$ and $f(x)>0$ $\forall x\in(a,b)$; $f(a)=f(b)=0$; prove that $b-a>\pi$.
104263
How to show that $f'(x)<2f(x)$
50833
Find all $f:\mathbb R\to\mathbb R$ such that $\forall x,y\in\mathbb R$ the given equality holds: $xf(y)+yf(x)=(x+y)f(x)f(y)$.
67292
Prove that $\lim_{t\to \infty} t\mu(\{x:f(x)\geq t\})=0$
13927
Values of $a$ s.t. for all continuous $f$ with $f(0)=f(1)$ there exists $x$ s.t. $f(x+a) = f(x)$