Separable equations (but more like integration questions)

AI Thread Summary
The discussion revolves around solving an initial-value problem using separable equations, specifically the equation 8cos^2y dx + csc^2x dy = 0. The user seeks clarification on integrating terms like 8/csc^2x and 1/cos^2y, expressing uncertainty about whether this knowledge is expected after completing Calculus II. Responses suggest using trigonometric identities for integration, such as converting to sin^2 and secant squared forms. The user is encouraged to apply these identities and techniques to their specific integration problems. Overall, the thread emphasizes the importance of trigonometric identities in solving differential equations.
Beez
Messages
32
Reaction score
0
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!
 
Physics news on Phys.org
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.
 
Last edited by a moderator:
Thank you

Thank you very much for the quick response.
I will try to solve the problems with the reference you provided.
 
Post again if you want a more thorough explanation.
 
I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
Thread 'A cylinder connected to a hanging mass'
Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
Back
Top