Proof that the exponential function is the only solution to dy/dx = y, y(0) = 1
1440
Are the any non-trivial functions where $f(x)=f'(x)$ not of the form $Ae^x$
138054
Proving that $\int_0^1 f(x)e^{nx}\,{\rm d}x = 0$ for all $n\in\mathbb{N}_0$ implies $f(x) = 0$
65077
Differential Equations, unique solution
145504
Help solving variable separable ODE: $y' = \frac{1}{2} a y^2 + b y - 1$ with $y(0)=0$
88442
Prove that there's no ordered basis $E$ in which $T{x\choose y}={0\choose y}$ can be represented as $1\ 2\choose 2\ 4$
123724
Solve $(y')^2 - xy' + y = 0$
6937
General solution to the PDE $xU_x+yU_y=0$
40875
Particular solution of $y''-4y'+5y = 4e^{2x} (\sin x)$
106609
Show that $e^{iy} = 1 + iy + \frac{\mu_1 y^2}{2}$ for all $y \in \mathbb{R}$ with $|\mu_1| \leq 1$
86193
Rigorous proof that $dx dy=r\ dr\ d\theta$
55210
Prove that the equation: $c_0+c_1x+\ldots+c_nx^n=0$ has a real solution between 0 and 1.
14656
The differential equation $xu_{x}+yu_{y}=2u$ satisfying the initial condition $y=xg(x),u=f(x)$
155864
Prove or disprove: if $y'=y-y^2$ and $y(0)=a$ where $00$
152472
How to get solutions in elementary functions to the following non-linear ODE
118462
How to solve this first-order differential equation?
116946
Ordinary differential equation $y'(t)=\sin(f(t,y))$
75390
How does one prove that if function's partial derivative respect to every variable is zero, function is constant?