Table of Contents
Additional Resources
NARROW DISPLAY WARNING
You are most likely using a tablet or mobile device in portrait orientation. This website is best viewed using a typical computer screen with the browser window maximized.
Viewing this website in portrait orientation can cause problems with equations being longer than the screen width (you can scroll to the right), images being poorly sized, and the font size of maths text being much smaller than regular text. If your only option is a tablet or mobile device, your viewing experience will be better if you view this website in landscape orientation. You might need to refresh the page to fix any problems after rotating.
A lot of students don't realize this, but WolframAlpha can be used to check your work on maths homework. I say check because you don't want to use WolframAlpha to do your homework for you. If students don't actually do the homework themselves, those students tend to do very badly on exams because they didn't practice by doing the homework. Copying answers from anywhere will complete the assignment but you won't retain much for the exam. Despite homework counting for around 10% of the course usually, about 90% of learning happens when doing the homework. Don't sabotage yourself by not doing your homework.
WolframAlpha can do a lot a common problems if you know how to type the problem in correctly. One major difficulty is WolframAlpha will try to simplify the answer in a way a person would not, making the result significantly different from what a person would write. Also, complicated problems can exceed the free computation time limit and you may not get an answer. You can get around this by paying for a subscription, which also tries to provide step by step solutions, but the steps can be counter intuitive sometimes. However, the free version of WolframAlpha is often good enough.
The above link leads to WolframAlpha with the following input.
solve x = 1 + 1/y for y
Part of the output is
\begin{equation} y = \frac{1}{x-1} \text{ and } x \neq 1 \end{equation}The above link leads to WolframAlpha with the following input.
derivative of x^4 sin(x) e^x with respect to x
Part of the output is
\begin{equation} \frac{\text{d}}{\text{d}x} (x^{4} \sin(x) e^{x}) = e^{x} x^{3} ((x + 4) \sin(x) + x \cos(x)) \end{equation}The above link leads to WolframAlpha with the following input.
integral of x^4 sin(x) e^x dx
Part of the output is
\begin{equation} \int x^{4} \sin(x) e^{x} \text{ d}x = \frac{1}{2} e^{x} ((x^{4} - 6 x^{2} + 12 x - 6) \sin(x) - (x^{4} - 4 x^{3} + 6 x^{2} - 6) \cos(x)) + \text{ constant} \end{equation}The above link leads to WolframAlpha with the following input.
integral from 3 to 7 of x/(x^2+1) dx
Part of the output is
\begin{equation} \int_{3}^{7} \frac{x}{x^{2}+1} \text{ d}x = \frac{\ln(5)}{2} \end{equation}The above link leads to WolframAlpha with the following input.
plot direction field for y' + xy = 0
For legal reasons I have not shown the output here, but WolframAlpha does make direction field plots similar to your textbook.
The above link leads to WolframAlpha with the following input.
y' + xy = 0
Part of the output is
\begin{equation} y(x) = c_{1} e^{-x^{2}/2} \end{equation}The above link leads to WolframAlpha with the following input.
y' + xy = 7x with y(0) = 2
Part of the output is
\begin{equation} y(x) = 7 - 5 e^{-x^{2}/2} \end{equation}The above link leads to WolframAlpha with the following input.
use Euler method y' = 2*x-y, y(0) = 0, from 0 to 1, h = 0.1
Part of the output is
| step | x | y |
|---|---|---|
| 0 | 0.0 | 0.0 |
| 1 | 0.1 | 0.0 |
| 2 | 0.2 | 0.02 |
| 3 | 0.3 | 0.058 |
| 4 | 0.4 | 0.1122 |
| 5 | 0.5 | 0.18098 |
| 6 | 0.6 | 0.262882 |
| 7 | 0.7 | 0.356594 |
| 8 | 0.8 | 0.460934 |
| 9 | 0.9 | 0.574841 |
| 10 | 1.0 | 0.697357 |
The above link leads to WolframAlpha with the following input.
y''+y=0, y'(0)=-1, y(0)=4
Part of the output is
\begin{equation} y(x) = 4\cos(x)-\sin(x) \end{equation}The above link leads to WolframAlpha with the following input.
{{5,-2},{7,-4}}
which is how a matrix is inputted into WolframAlpha. The exterior curly braces formed the matrix and each set of curly braces inside specifies a row of the matrix.
\begin{equation} \begin{bmatrix} 5 & -2 \\ 7 & -4 \end{bmatrix} \end{equation}Part of the output is
\begin{equation} \lambda_{1} = 3 \quad \vec{v}_{1} = \begin{bmatrix} 1 \\ 1 \end{bmatrix} \qquad \lambda_{2} = -2 \quad \vec{v}_{2} = \begin{bmatrix} 2 \\ 7 \end{bmatrix} \end{equation}