Tagged Questions

2
votes
0answers
43 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 ) ...
5
votes
3answers
152 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 ...
1
vote
0answers
115 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 ...
1
vote
1answer
210 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 ...
2
votes
1answer
215 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 ...