How to prove any solution of the equation $y''+f(x)y=0$ is bounded on$(0,+\infty)$? Here $f(x)$is increasing and positve on$[0,+\infty)$.
101776
Bounded solution for an equation
20192
Prove that: $(f(x))^{2} + (f'(x))^{2} \leqslant \max(a,b)$ where $(a,b) \in \mathbb{R}^2$
19986
How can this be proved $\lim_{x\to\infty}(f(x)+f'(x))=l$
155864
Prove or disprove: if $y'=y-y^2$ and $y(0)=a$ where $00$
144322
Prove for bounded $f$, if $f:[a,r] \to \mathbb{R}$ is Riemann-Integrable for $r \in [a,b)$ then $f:[a.b] \to \mathbb{R}$ is Riemann-Integrable
82745
Showing Entire Function is Bounded
114747
If $\lim_{x \to \infty}f'(x)=+\infty$ then $\lim_{x \to \infty}(f(x)-f(x-1))=+\infty$ and $\lim_{x \to \infty}f(x)=+\infty$.
145368
How to show $f:Y\to X^{+}$ is continuous?
76679
Prove there are no other solutions of functional equation $f(x+y) = \frac{f(x)+f(y)}{1-f(x)f(y)}$
22303
How do I prove that $f(x)f(y)=f(x+y)$ implies that $f(x)=e^{cx}$, assuming f is continuous and not zero?
21954
A question about $f(x)\equiv 0$
86409
Show that $\lim_{x \to +\infty}\left(f(x)+f'(x)\right)=0 \Rightarrow \lim_{x \to +\infty} f(x)=0$
34187
The limit of the derivative of an increasing and bounded function is always $0$?
55210
Prove that the equation: $c_0+c_1x+\ldots+c_nx^n=0$ has a real solution between 0 and 1.
31732
If the function $f$ satisfies the equation $f(xf(y)+x)=xy+f(x)$, find $f$
113151
Does $\sum\limits_{i=1}^{\infty}|a_i||x_i| < \infty$ whenever $\sum\limits_{i=1}^{\infty} |x_i| < \infty $ imply $(a_i)$ is bounded?
136475
d'Alembert-like functional equation: $f(x+y)+g(x-y)=\lambda f(x)g(y)$