Find general solution of $xx''=(x')^3$

Let $T,U:V\to W$ be linear transformations. Prove that if $W$ is finite-dimensional, then $\text{rank}(T+U)\leq\text{rank}(T) + \text{rank}(U)$.

Find the value of $a$ where $a^x = \frac{\log(x)}{\log(a)}$ has only one solution

What can the range of a measure be?

Determine hollow marble with least number of weighings

Solve $\lfloor{\sin x}\rfloor+\lfloor{\cos x}\rfloor=2^{1-|\sin x|}$

What is the meaning of "in particular" in this proof?

Generators for the ideal of entire functions vanishing on $\mathbb Z\times\mathbb Z\subset \mathbb C\times\mathbb C$

Proving a complicated looking inequality in a simple way

Prove that $N \subseteq H$

Prove that all ideals in $\mathbb{Z}[x]$ are generated by two elements.

On Ramanujan's approximation, $n!\sim \sqrt{\pi}\big(\frac ne\big)^n\sqrt [6]{(2n)^3+(2n)^2+n+\frac 1{30}}$

Let $H$ be a subgroup of $G$, and suppose that $G$ acts by multiplication over the set $X:=G/H$ of the left-hand side classes of $H$ over $G$.

Related