Tagged Questions
0
votes
1answer
43 views
How to solve $a \frac{d^2 y}{d x}+b \frac{d y}{d x} = f(y)$?
Let $a,b$ be real numbers and $y$ is a function of $x$.
$f$ is a given function.
How to solve the ODE :
$a \dfrac{d^2 y}{d x}+b \dfrac{d y}{d x} = f(y)$ ?
Can it be done in closed form ?
2
votes
0answers
71 views
A photon in expanding Universe (a snail on a tree)
I want to know how far a snail can reach in expanding universe. It has a constant speed c = 1 and tree is expanding at speed $v= H_0 D$, with Hubble constant $H_0 = 1$. Here D(T) is the distance of ...
5
votes
1answer
158 views
Tough Inverse Fourier Transform
In reference to this answer I gave the other day, I came across a very interesting function whose IFT would be nice to evaluate as part of completing the solution to the problem I answered. The ...
9
votes
0answers
170 views
Addition formula for $f_n(x+y)$ in closed form.
$n$ is a positive integer.
$$f_n(x)^n+\left(\frac{df_n(x)}{dx}\right)^n=1$$
$f_n(0)=0$,
$f_n'(0)=1$ then
I am looking for the addition formula for $f_n(x+y)$ in closed form.
if $n=1$ then
...
1
vote
1answer
136 views
Closed-form solution for this system of ODEs
I am trying to solve the following system (derived from a Michaelis-Menten kinetics model for an enzymatic chemical reaction):
$$\dot{y}_a = r_p x_a - \lambda_p y_a$$
$$\dot{x}_b = \frac{\alpha_0 + ...
