All Questions
7
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
2
votes
1
answer
58
views
Exponential populations that depend upon each other
I have a question about how to solve an exponential problem that involves two populations, each which depends on the other.
For example, let's say we have an initial population of $h$ humans that ...
- 153
0
votes
0
answers
69
views
differential equation of a population growth and change - another question
I formulate a system of equations and initial conditions of the following data:
Each year the population1 grows by 4% and population2 by 2%.
Also each year 3% of population1 leaves it and go to ...
- 1,298
0
votes
2
answers
266
views
differential equation of a population growth and change
I want to formulate a system of equations and initial conditions of the following data:
Each year the population1 grows by 4% and population2 by 2%.
Also each year 3% of population1 leaves it and go ...
- 1,298
1
vote
1
answer
344
views
Solution of $d^2u/dx^2 + u/A = 0 \ (\text{or } \ C),$ with conditions
Does the following ODE:
$$d^2u/dx^2 + u/A = 0 \quad (\text{or } \ C),$$
have a solution with the conditions:
$$
\left.\frac{d^2u}{dx^2}\right|_{x=0} = 0,
$$
$$u(x=0) = B$$ and
$$
\left.\frac{du}{...
- 343
0
votes
1
answer
111
views
How to solve this system of ODE's?
I'm not sure how to proceed to solve this system of ODE's;
$$ \begin{bmatrix}\dot{x}_1 \\\dot{x}_2\end{bmatrix}=\begin{bmatrix} \cos t & -\sin t\\ \sin t & \cos t \end{bmatrix}\begin{...
- 3,342
0
votes
2
answers
125
views
Linear system of ODEs
Given is the ODE system
$y'=\left(\begin{matrix}1\\1\\0\\ \end{matrix}\right)+\left(\begin{matrix}0&0&0\\0&k&0\\0&-k&k\\ \end{matrix} \right)y$
with boundary conditions $y(T)...
- 5