All Questions
3
questions
5
votes
3
answers
1k
views
Solve the differential equation that define exp(x)
In the wikipedia page for the exponential function in the "formal definition" section I found this statement:
Solving the ordinary differential equation $y'(x)=y(x)$ with the
[initial ...
- 277
2
votes
1
answer
107
views
How do we know $\lim_{t\rightarrow \infty }e^{-st + 4t} = 0 ? $
I'm trying to evaluate an integral, and the final step is to evaluate $e^{-st + 4t}$ at infinity minus $e^{-st + 4t}$ at $10$. (The limits of integration were $\infty$ and $10$.)
To evaluate the ...
- 2,331
0
votes
1
answer
499
views
An ODE with boundary conditions at infinity
I have a problem where:
$\ddddot{x} - 2 \ddot{x} + x = 0$
With boundary conditions
$x(0) = 1, \dot{x}(0) = 2, x(\infty) = 0, \dot{x}(\infty) = 0$
So I get my characteristic equation:
$s^4 -2s^2 + ...
- 227