All Questions
Tagged with ordinary-differential-equations exponential-function
235
questions
3
votes
2
answers
648
views
Constructing a differential equation for hyperbolic crochet
There is plenty of information about hyperbolic geometry and its melding with crochet, however I have yet to find an exact equation for determining the number of stitches in each row. I will try to ...
- 41
0
votes
4
answers
1k
views
Finding a differential equation when a half life is known
Does anyone know how I would write a differential equation for the following? I am not interested in the answer as such, I'm more interested in the steps and how to obtain the answer. I don't know how ...
- 79
0
votes
1
answer
414
views
Commuting Exponential Matrices
Let $x(t)=\exp(tA)\exp(tB)$ and $y(t)=\exp(t(A+B))$.
Show that if $AB=BA$ then $x(t)$ and $y(t)$ satisfy the same initial value problem for ODEs and therefore must be equal.
$A, B$ square matrices.
- 269
1
vote
2
answers
71
views
Please help to solve this ODE with function coefficients
Is it possible to solve this ODE for $y$? According to wikipedia this falls in the category of a first order, linear, inhomogeneous ODE with function coefficients. But is there a more tractable ...
- 2,155
2
votes
0
answers
73
views
differential operator
I've read journal "On the Comparison of Several Mean Values: An Alternative approach" (Welch, 1951). I don't understand this expression:
$$E\left(\exp\left[ \sum_t ( w_t - \omega_t ) D_t\right]\right),...
7
votes
3
answers
430
views
What are other solutions to this differential equation, "similar" to $\sin x$ and $e^x$?
I've been studying electronics, where they make great use of the relationship between the sine and exponential functions ($e^{i \omega t} = \cos{\omega t} + i \sin \omega t)$. This relationship is ...
- 389
1
vote
0
answers
263
views
maple code for exp-func. for solving PDE's & non-linear ODE's?
How can I create the Maple code using exponential-function solving the equation below?
$u_t = \gamma u_x+6u(u_x)^2+(3u^2-1)u_{xx}-u_{xxxx}$
$u_t =u_{xx}-u^3+u,$
$\alpha u''(x) = \beta u(x)(u(x)-m)(...
- 184
1
vote
1
answer
222
views
Need to deduce $f(x)$ from $f_x=e^{t(x)}$
I know that
$$f_x=e^{t(x)}$$
(where the notation $f_x=\frac{df}{dx}$)
(EDIT: $f=f(x)$ and $t$ parameterizes $x$, so $x=x(t) \Leftrightarrow t=t(x)$)
and that therefore
$$\frac{d^n f_x}{dx^n}=\...
- 2,155
2
votes
1
answer
4k
views
Fundamental matrix and exponential of matrix using Laplace Transform
I'm trying to work out how to find $$\exp(At)$$ for a system of linear differential equations $$x'=Ax.$$
I know that the solution is a fundamental matrix of the system such that $$\exp(At)=I$$
at ...
- 1,146
132
votes
9
answers
27k
views
Prove that $C e^x$ is the only set of functions for which $f(x) = f'(x)$
I was wondering on the following and I probably know the answer already: NO.
Is there another number with similar properties as $e$? So that the derivative of $ e^x$ is the same as the function itself....
- 1,647