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March 20th, 2012, 11:56 PM   #1
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Differentiation trouble

I am having trouble with these:

-y = 1/(3 + x^2)<--denominator is under square root.
-dy/dx: -x/(y(x)^3)
-y(x)^2 + x^4y'(x)^2 = 1 <--the second y is prime
-y''(x) + 2y'(x) + 5y(x) = 0 <-- The first y is 2 prime and the second y is prime

I have a final on monday and am trying to understand these the best I can

P.S. Does anybody know of a site that can teach me how to express these equations on the computer to make them look authentic to the original?
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March 21st, 2012, 05:32 AM   #2
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Math Focus: Calculus/ODEs
Re: Differentiation trouble

1.)

To differentiate, use the power and chain rules:



2.)

Separate variables and integrate:





The solution is given implicitly by:



3.)

Separate variables and integrate:







4.)

This is a second order homogeneous equation whose associated auxiliary equation has the roots:



Hence, the general solution is given by:



Do a search here and on the web for LaTeX to see how to write math expressions.
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