Show with only elementary methods that the ODE $f(x)=f'(x), f(0)= 0$ has only the constant function as solution
10431
Prove that $C\exp(x)$ is the only set of functions for which $f(x) = f'(x)$
123731
Plotting the solution of a differential equation with its derivative
30204
Prove that $f'(0)$ exists and $f'(0) = b/(a - 1)$
107727
$m\{x\in [0,1]:f'(x)=0\}>0$
130322
Show that $f(x) = 0$ if $x = 0$ $f(x) = \text{exp}(-1/x^{2})$ if $x \neq 0$ is infinitely differentiable but not analytic at $x_{0} = 0$ `
152472
How to get solutions in elementary functions to the following non-linear ODE
149344
Solve a differential equation and evaluate the solution at a particular value of independent variable
127582
Solving of a seperable differential equation
89537
$ \int_0^x f(t)dt=\int_0^{ax}f(t)dt+ \int_0^{bx}f(t)dt$ implies $f$ constant
72872
Number of zeroes of solution to $y''(x)+e^{x^2}y(x)=0$ in $[0,3π]$
4636
How to show that $f$ is differentiable at $x=0.$
75390
How does one prove that if function's partial derivative respect to every variable is zero, function is constant?
74583
Prove that $f'(0)=L$.
139419
Problem on the domain of the solution of a differential equation
30697
Solution of a Riccati ODE
158938
Using DSolve to solve for x[t,parameter]
105068
Proving that the function is differentiable and $f'(0)=0$