Separable equations (but more like integration questions)

[Beez]

Hi, I have just started my differential equations class. To solve the initial-value problem, 8cos^2ydx + csc^2xdy = 0 (initial condition: y(pai/12) = (pai/4) )using separable equations method, I have to change the equation to
8/csc^2dx + 1/cos^2ydy (Am I right so far?)

My problem is I don't know (or remember) how to integrate neither 8/csc^2dx nor 1/cos^2y. Am I suppose to do know how to calculate if I have finished Calculus II? I reviewed Trig. and Calculus textbooks to figure out how to calculate them but so far could not find even a similar problem.

I also have no idea how to integrate the followings:

a. x/secx dx
b. 1/cot^2x dx
c. 1/cos3y dx
d. 1/sec^3 10x dx

Any kind of help would be highly appreciated!

 

[whozum]

The first one, you want to put the x's on one side and the y's on the other. To integrate sin^2 and secant squared you'll want to use some trig identities.

\cos^2(x) = \frac{1}{2}(1+\cos(2x)). Others can be found http://www.math2.org/math/trig/identities.htm" .

a. xcosx dx, try parts.
b. tan^2x, translate to secant.
c. sec^3, translate sec^2 to tan^2+1
d. trig identities.

 

[Beez]

Thank you

Thank you very much for the quick response.
I will try to solve the problems with the reference you provided.

 

[whozum]

Post again if you want a more thorough explanation.