Hi

The following questions i need help on:

Solve the Differential Equations

1)

2)

u=2x du=2 dx

3)

what should i do next?

i tried but that didn't work.

P.S

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- August 28th 2010, 03:10 AMPaymemoneySeparable Differential Equations Problems
Hi

The following questions i need help on:

Solve the Differential Equations

1)

2)

u=2x du=2 dx

3)

what should i do next?

i tried but that didn't work.

P.S - August 28th 2010, 03:18 AMmathaddict
- August 28th 2010, 04:48 AMPaymemoney
question 1) and 2) are incorrect according to the book's answers.

The book's answers say the following:

1)

2) - August 30th 2010, 12:48 AMPaymemoney
can anyone help me??

- August 30th 2010, 02:33 AMraj007

so

- August 30th 2010, 03:46 AMAckbeet
Your algebra for (1) is incorrect. As far as I can tell, your mistake was in going from step 1 to step 2. Try this:

Integrate, etc.

As for the second problem, your answer and the book's answer are equivalent. You've just re-defined your constant of integration once or twice. Your constant is the negative of the book's constant. That is an unimportant difference.

As for #3, raj007's solution is a bit bizarre, in my opinion. I would go with a straight-forward trig substitution, or look the integral up in a table if you're allowed to do that. - August 30th 2010, 06:46 AMAckbeet
Concerning Problem #3: My idea of trig substitution is not, I think, useful. Try partial fractions after factoring the denominator on the LHS.

- August 30th 2010, 04:32 PMPaymemoney

What should i do next? - August 30th 2010, 05:20 PMDefunkt
The cosine in your numerator dissappeared. A minus in the denominator has also gone astray.

And a shorter way will be to factor into and then do partial fractions. - August 30th 2010, 09:27 PMPaymemoney

what should be done next?? - August 30th 2010, 09:48 PMmathaddict
- August 31st 2010, 02:41 AMPaymemoney
oops my mistake it's meant to be:

- August 31st 2010, 03:03 AMPaymemoney
- August 31st 2010, 03:06 AMAckbeet
That looks good, except that in going from step 3 to 4, you lost your y-1 factor. And then in going from step 4 to step 5, you regained it! I wouldn't recommend dropping terms willy-nilly, unless you have a good reason for doing it (approximation, for example).

Recommendation: rename your constant of integration so it looks a bit cleaner. That is, define, say, K = exp(2C), and use K in both places there. This is not a fundamentally important aspect of the problem, however. It is merely cosmetic. - August 31st 2010, 03:11 AMAckbeet
To fix the sign error, I'd go back and re-visit your partial fraction decomposition. I think you might have those signs flipped.