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Old 09-02-10, 06:57 PM   #1
phantomcow2
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Is this integral correct?

I'm trying to solve a differential equation but am stuck on a specific step that involves integration. Could someone please explain how the following is true?



If we integrate both sides both sides with respect to t, I would have expected the following result:

1/(1+t^2) - 1/(1+1^2)*y = 3*arctan(t) + C

And factoring out the 1/(1+t^2) from the left, we would get [1/(1+t^2)](y-1). Solving for y becomes

-3*arctan(t)*(1+t^2) +1 + C = y


Why am I incorrect?
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Old 09-03-10, 08:36 AM   #2
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I'm not 100% sure your wxy Or, xyz statement is true, but I'm not much of a math guy as far as engineers are concerned.
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Old 09-03-10, 09:06 AM   #3
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This part of your equation makes no sense: 1/(1+1^2). One would simply write that as 1/2.
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Old 09-03-10, 11:57 AM   #4
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That second 1 is a lower case T.
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Old 09-03-10, 12:09 PM   #5
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I'm pretty sure the answer is 42



or possibly poo
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Old 09-03-10, 02:11 PM   #6
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That second 1 is a lower case T.
Looks like a one to me but yeah must have been a typo.
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Old 09-03-10, 03:42 PM   #7
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oops, good catch. The one should have been a lower case t. .

RUOkie, 42 couldn't possibly be a valid solution since the solution is a general one -- it doesn't pertain to a specific number.
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Old 09-03-10, 03:46 PM   #8
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RUOkie, 42 couldn't possibly be a valid solution since the solution is a general one -- it doesn't pertain to a specific number.
How can you get more general than the answer to life, the universe, and everything?
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Old 09-03-10, 03:58 PM   #9
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oops, good catch. The one should have been a lower case t. .

RUOkie, 42 couldn't possibly be a valid solution since the solution is a general one -- it doesn't pertain to a specific number.
then it has to be "poo" by process of elimination. next question please.
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Phobias are for irrational fears. Fear of junk ripping badgers is perfectly rational. Those things are nasty.
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Old 09-03-10, 05:07 PM   #10
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Are you asking how the last line in the image is correct? The integral of d/dt (X) with respect to t = X (integral of a derivative of X = X). That is y/1+t^2 in your example. You already agree with the right side integral solution so now you just need to multiply both sides by 1+t^2 to solve for y.
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