This is surely the simplest problem imaginable in DE, but it's been a few years and I'm having trouble recalling. The goal of my task doesn't necessitate relearning DE, so I thought I would take a shot at asking directly.
Simply, I wish to express the time-dependent rate equation...
I've uploaded my attempted solution here. The problem I'm having is highlighted at the bottom in red.
The issue I'm having is expressing the direction of H. I realize the cancellation that occurs at point (0,0,z), where the only the z-component of the H-field remains. I also realize that my...
This is just a general question regarding Boolean minimization.
Expression:
Y=\bar{X}_1\bar{X}_0+\bar{X}_1X_0+X_1\bar{X}_0
Minimized expression:
Y=\bar{X}_1+\bar{X}_0
My first attempt was to minimize it algebraically. I factored \bar{X}_1 from the first two terms, then the \bar{X}_0+X_0...
Beautiful.
Inverting both sides did the trick.
Inverse of the RHS is \begin{bmatrix}\frac{-5}{13} & \frac{2}{13} \\ \frac{4}{13} & \frac{1}{13} \end{bmatrix}. I'll call this B^{-1}
So then I'm left with
\begin{align}I+2A&=B^{-1} \\
2A&=B^{-1}-I \\...
Inverse of a sum of matrices [solved]
The problem is relatively simple. Given the equation:
(I+2A)^{-1}= \begin{bmatrix}
-1 & 2 \\
4 & 5 \end{bmatrix}
Find A.
My problem seems to be that I'm distributing the inverse on the LHS incorrectly. My real question then is, is the...
Thanks to all who responded.
I believe I was doing my computations incorrectly. I am given voltage:
100e^{-500t}V
And current:
20-20e^{-500t}mA
Power being the product:
2e^{-1000t}(e^{500t}-1)W
And derivative:
-1000e^{-1000t}(e^{500t}-2)
To find out when power is...
I'm trying to calculate maximum power. Once I computed power as a function of time I took its derivative and set it equal to zero. Now it need to solve for time and I can't seem to get it done. What I have is...
-1000e^{-500t}-2000e^{-1000t}=0
My first inclination is to use ln, but ln(0)...
I need to solve for t and it's slipped my mind how to manipulate this.
\frac{1}{4}=te^{-8t}
to
ln(1/4)=lnt-8t
I understand the laws of logs (I think), but I still can't seem to isolate the t.
From what I understand you are correct, an equation with n derivatives requires n initial conditions. Not too sure if the same applies for coupled DEs though.
In order to determine what the integrating factor is you must first normalize the equation.
\frac{dy}{dx}+P(x)y=f(x)
is an example of a normalized differential equation, the IF being
e^{\int P(x)dx}.
Does this help?
You are both absolutely correct. I was the end of my study session, there should definitely be an equation there. I'll be posting it as soon as I can get to the book.
@arildno - I know this doesn't help right now, but the problem is to be solved using Laplace transforms, not undetermined...