DE: Inspection for R(x)=sinx or cosx

  • Thread starter median27
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In summary, the conversation discusses the use of solved problems with given conditions in Advanced Engineering Mathematics, specifically in the topic of Differential Equations. The conversation also addresses sign conventions and formulae for solving equations involving sine and cosine. The correct formula for solving sine and cosine conditions is mentioned.
  • #1
median27
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Can you post solved problems using these conditions? We're on the Advanced Engineering Mathematics and reviewing our Differential Equations. My professor only introduces this topic and didn't went deeper. I'm troubled about the sign convention, e.g.:

(D^2-9)y=-sin4x
(D^2-a^2)y=sinbx
yp=-sinbx/(a^2+b^2)
a=3, b=4
yp=sin4x/(3^2+4^2)
yp=sin4x/25

how does yp became positive? What are the formulae used... also for cosine condition?

Thanks for your help!
 
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  • #2
hi median27! :smile:

(try using the X2 icon just above the Reply box :wink:)
median27 said:
I'm troubled about the sign convention …

it's not a convention, it's just the correct formula …

D2(sin4x) = -16sin4x

so (D2 - 9)(sin4x) = (-16 - 9)sin4x = -25sin4x :wink:

(same for cos4x)
 
  • #3
Your formula tells you the particular solution of

(D2-32)y = +sin 4x

is
[tex]y_p = -\frac{\sin 4x}{3^2+4^2}[/tex]
But that's not the differential equation you have. Yours has a negative sign in front of the forcing term, so you must flip the sign of the particular solution.
 
  • #4
can you give me the correct formula to use for sine and cosine?

(D^2-a^2)y=sinbx
yp=-sinbx/(a^2+b^2)... is it the standard formula for sine condition?
 
  • #5
you can work it out for yourself …

if y = Ksinbx, when will (D2 - a2)y equal sinbx ? :smile:
 
  • #6
Alright, i get it. Thanks
 

1. What is the purpose of an inspection for R(x)=sinx or cosx?

The purpose of an inspection for R(x)=sinx or cosx is to determine if the given function satisfies specific criteria, such as continuity, differentiability, and periodicity.

2. How is an inspection for R(x)=sinx or cosx performed?

An inspection for R(x)=sinx or cosx involves analyzing the given function and its properties, such as its graph, domain, range, and any transformations applied. It may also involve taking derivatives to check for differentiability.

3. What are the key properties of R(x)=sinx or cosx that are checked during an inspection?

The key properties that are checked during an inspection for R(x)=sinx or cosx include continuity (if the function is defined at all points), differentiability (if the function has a derivative at all points), and periodicity (if the function repeats itself after a certain interval).

4. What are some common errors to look out for during an inspection for R(x)=sinx or cosx?

Some common errors to look out for during an inspection for R(x)=sinx or cosx include mistaking the period of the function, incorrectly identifying the domain and range, and forgetting to check for differentiability.

5. Can an inspection for R(x)=sinx or cosx be applied to other trigonometric functions?

Yes, an inspection for R(x)=sinx or cosx can also be applied to other trigonometric functions, such as tanx, secx, cscx, and cotx. The key properties that are checked may differ slightly, but the overall process is similar.

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