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ODE undetermined coefficients

ODE undetermined coefficients

Postby macleanl » Sun Oct 23, 2011 6:14 am
ok so i have the following problem

y" + 4*y' +3*y = x^2*e^(-2*x)

my issue is finding the particular solution, i have no issues with the homogenous solution
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Re: ODE undetermined coefficients

Postby Paepaok » Mon Oct 24, 2011 11:45 pm
You can't find the particular solution without some values, in your case, for y and for y′ (e.g., y(1)=2 and y′(-3)=20). Then you would substitue these values in and find the values of the constants of integration.
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Re: ODE undetermined coefficients

Postby williamthomas » Sun Jan 15, 2012 9:42 pm
Are you people using WA to solve math problems? Do you have a special widget or a program to do this or do you just use the search engine for this?
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Re: ODE undetermined coefficients

Postby Nuclearman » Tue Jan 17, 2012 6:16 am
Sorry to usurp this conversation, but thought I'd answer William's question.

williamthomas wrote:Are you people using WA to solve math problems? Do you have a special widget or a program to do this or do you just use the search engine for this?


Your new to W|A, so you probably don't understand that this is one of the intended uses of W|A. It is not intended to be used like a search engine, as they perform two very different, but very complimentary things. W|A does it's best to give you the quantitative "facts" to your query. A search engine simply gives you links to sites that contain your query. The difference being that the idea of W|A is to give you a list of facts relating to your query, while a search engine simply gives you related websites. General guidelines as to when to use each is as followed: If you are seeking "facts", use W|A. If you are seeking "information", use a search engine.

W|A cannot (yet) tell you about "people of united kingdom" (currently things your looking for the population). However, it can give you facts and figures about the "united kingdom", such as it's total land area (little over 94,000 square miles), it's population (almost 62 million people) it's currency name (British pound), GDP (around 2.25 trillion US Dollars). If that is not the kind of "facts" you were looking for, you can refine your query. You can look for something related to the united kingdom, such as "United Kingdom Armed Forces", and discover that the UK has about 112,000 people in the army, 39,000 in the navy and 43,700 in the air forces, along with a nuclear stockpile of 180 warheads. W|A at it's core is an engine for math computations, that is being expanded to someday compute anything purely limited to what the user wants to compute, it doesn't even exactly have to have a purpose. Such as "what is the 10,000th word in Hamlet?" (not currently answerable, but consider what it knows about "Hamlet" it isn't far off)

Though that is but the tip of the iceberg. W|A is only limited to the data that it has curated (a term it uses for data formatted in such a way it can use it) and stored. One needs to visit the examples section just to get an idea of what has been curated, http://www.wolframalpha.com/examples/. It's an impressive list, but it should be noted that those are simply "examples" and do not show the true limits of the site. One could spend weeks telling the full scope of W|A. Been around for a while, and I learn new things about it often enough.
-Nuclearman
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