I have a few questions about finding the general solution of first-order linear differential equations..

please help, I have no clue!! =/

http://i28.tinypic.com/2yv3343.gif

http://i31.tinypic.com/2818w02.gif

http://i28.tinypic.com/n81ee.gif

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- Apr 19th 2008, 11:10 PMiloveyou33linear differential equations??
I have a few questions about finding the general solution of first-order linear differential equations..

please help, I have no clue!! =/

http://i28.tinypic.com/2yv3343.gif

http://i31.tinypic.com/2818w02.gif

http://i28.tinypic.com/n81ee.gif - Apr 19th 2008, 11:14 PMJhevon
the integrating factor method takes care of all these. see post #21 here

- Apr 19th 2008, 11:20 PMiloveyou33
it doesn't make sense though..

is there a simpler way of explaining it?

I don't understand what "the integrating factor" is in the first place.. - Apr 19th 2008, 11:33 PMJhevon
it is just something you multiply through by to make the left hand side the derivative given by the product and the integrating factor. for the first one:

(with practice, you will be able to recognize the integrating factor immediately, but let's go through the method to see it)

the integrating factor is

multiply through by the integrating factor, we get:

now the left hand side is the result of differentiating by the product rule, thus

integrate both sides, we get:

the others are done similarly - Apr 20th 2008, 09:51 AMKrizalid
- Apr 20th 2008, 10:44 AMJhevon