Prove that $y'=-y^3+\sin x $ has a unique solution satisfying $y(0)=y(2\pi)$
158444
Is this periodic solution unique? (ODE)
124208
Proof $|\sin(x) - x| \le \frac{1}{3.2}|x|^3$
154829
How to solve $y'' + y = y^{-3}$
71465
solution of $y' = \exp \left(-\frac yx\right) + \frac yx$
75888
How to prove the function $y = \sin x$ is not a closed function?
143050
If $\tan(\frac{\pi}{4}+\frac{y}{2})=\tan^3(\frac{\pi}{4}+\frac{x}{2})$,then prove that $\sin y=\frac{\sin x(3+\sin^2 x)}{(1+3\sin^2 x)}$
6937
General solution to the PDE $xU_x+yU_y=0$
69172
$y'=$ ${-x+\sqrt{(x^2+4y)}}\over 2$ , $y(2)=-1$
3621
How can I show that $y'=\sqrt{|y|}$ has infinitely many solutions?
46028
Show that the solution for the Diophantine equation $x^2 - y^2 = N$ is unique if and only if $|N|$ or $\frac{|N|}{4}$, respectively, is $1$ or prime.
91003
Prove that equation has exactly 2 solutions
65000
prove that $x^2 + y^2 = z^4$ has infinitely many solutions with $(x,y,z)=1$
116946
Ordinary differential equation $y'(t)=\sin(f(t,y))$
74452
On a uniqueness proof for solutions of $\ a + x = b\,$ in a group
123724
Solve $(y')^2 - xy' + y = 0$
114307
Are Exponential and Trigonometric Functions the Only Non-Trivial Solutions to $F'(x)=F(x+a)$?
14656
The differential equation $xu_{x}+yu_{y}=2u$ satisfying the initial condition $y=xg(x),u=f(x)$