Basic help with Mathematica 5.2, please?

[*best&sweetest*]

I have just bought student edition of Mathematica and I have no idea how to so some basic stuff. Could anybody please tell me how to "sketch several typical solutions of the given differential equation and highlight the one that satisfies the initial condition" using Mathematica? I have tried looking at Wolfram website but couldn't find clear explanation.
Could you please give me some example of the code for any differential equation and any initial condition you want.
Technology is so not my thing.
Thanks!

 

[FredGarvin]

Why don't you start learning how to use the software? It's a pretty straightforward program once you learn the basics.

Take a look here for plenty of examples.
http://www.me.rochester.edu/courses/ME201/webexamp/exam.html

 

[tacman]

Sure, I'd be happy to help with some basic tasks in Mathematica 5.2. First, let's start by opening Mathematica and creating a new notebook. You can do this by going to File > New > Notebook. In the new notebook, you can enter the code for your differential equation and initial condition. For example, let's say we have the differential equation y''(x) + 2y'(x) + y(x) = 0 and an initial condition y(0) = 1, y'(0) = 0.

To sketch several solutions and highlight the one that satisfies the initial condition, we can use the command DSolveValue. The code would look like this:

DSolveValue[{y''[x] + 2y'[x] + y[x] == 0, y[0] == 1, y'[0] == 0}, y[x], x]

This will give us the general solution to the differential equation, and we can then plot it using the command Plot. For example:

Plot[%, {x, 0, 10}]

The % symbol refers to the output of the previous command, so in this case it would be the general solution. This will give us a plot of the solution with the initial condition highlighted.

I hope this helps get you started with using Mathematica for differential equations. If you have any further questions or need clarification, please don't hesitate to ask. Best of luck with your studies!