All Questions
4
questions
1
vote
0
answers
31
views
$f(x) = \sum_{j=1}^{4}c_{j}e^{r_{j}x} \quad \text{and} \quad g(x) = \sum_{j=1}^{4}d_{j}e^{s_{j}x}$. How to determine $c_{j},d_{j}$?
Let $\alpha_{i},\beta_{i} \in \mathbb{C}$, $\forall i= 1,2$ and $0 < a < b < \infty$.
\begin{align}
&f^{\prime \prime} + \alpha_{1} f = \alpha_{2} g^{\prime} \quad \text{in} \quad [a,b] \\...
- 657
0
votes
1
answer
202
views
Radio active decay formula is not growth formula, $p = p_0 * e^{kt}$, what is the formula for radio active decay, and why?
Trying to solve this question:
A radioactive material is known to decay at a yearly rate proportional to the amount at each moment. There were 2000 grams of the material 10 years ago. There are 1990 ...
- 671
1
vote
1
answer
80
views
Why does $u=e^{-i\omega x}e^{-k\omega^2t}$ "clearly" solve the 1-D heat equation?
So one of my least favorite things that textbooks do is using the words "clearly", "it should be obvious", etc.
In my PDEs class, we've started the Fourier Transform, and I missed the first day of it ...
- 2,429
1
vote
0
answers
263
views
maple code for exp-func. for solving PDE's & non-linear ODE's?
How can I create the Maple code using exponential-function solving the equation below?
$u_t = \gamma u_x+6u(u_x)^2+(3u^2-1)u_{xx}-u_{xxxx}$
$u_t =u_{xx}-u^3+u,$
$\alpha u''(x) = \beta u(x)(u(x)-m)(...
- 184