Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
JenniferSmart1
Group Title
For \[y''+y'2y=sinx\]
\[y_p=Acosx+Bsinx\]
why is it incorrect to guess:
\[y_p=Asinx\]
 2 years ago
 2 years ago
JenniferSmart1 Group Title
For \[y''+y'2y=sinx\] \[y_p=Acosx+Bsinx\] why is it incorrect to guess: \[y_p=Asinx\]
 2 years ago
 2 years ago

This Question is Closed

experimentX Group TitleBest ResponseYou've already chosen the best response.2
y_p doesn't contain constants of integration.
 2 years ago

JenniferSmart1 Group TitleBest ResponseYou've already chosen the best response.0
@experimentX , what do you mean by that?
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.2
what's the difference between solution of \( y''+y'2y=0 \) and \( y''+y'2y=\sin x \)
 2 years ago

JenniferSmart1 Group TitleBest ResponseYou've already chosen the best response.0
one has a particular solution and the other doesn't
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.2
for second order equation, you should have 2 constants of integration ... first one will have two constants .. now if you put another constant to particular solution ... and you will have 3 constants
 2 years ago

JenniferSmart1 Group TitleBest ResponseYou've already chosen the best response.0
could you illustrate that? sorry :S
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.2
dw:1352301416695:dw
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.2
guessing particular solution is quite difficult job ... easy when you have polynomials one the RHS. probably you are seeking this method http://en.wikipedia.org/wiki/Method_of_undetermined_coefficients
 2 years ago

JenniferSmart1 Group TitleBest ResponseYou've already chosen the best response.0
makes sense. Thanks!
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.2
the particular solution will be of the form \[ y_p=A\cos x+B\sin x \] you have to find the values of A and B by plugging into equation. I probably understand your Q quite clearly now.  plug \( y_p = A \sin (x) \) into DE, you have \[ y'' = \sin(x) \text{ and } y'(x) = \cos(x) \] no matter what the value of constant's ... there is no Cos(x) on RHS ... you cannot simply have Yp = A sin(x)
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.2
honestly i would prefer "Reduction of Order" or "Annihilation Operator" method .. they are quite faster than "Undetermined coefficients"
 2 years ago

JenniferSmart1 Group TitleBest ResponseYou've already chosen the best response.0
Example 1's y_c is that in the above attachment, but how is that relevant when example 1 is y''+y'2y=x^2 ??? I guess I'll just stick with "seeing patterns" and memorization :P
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.2
well ... the second case http://en.wikipedia.org/wiki/Method_of_undetermined_coefficients#Typical_forms_of_the_particular_integral
 2 years ago

JenniferSmart1 Group TitleBest ResponseYou've already chosen the best response.0
Oh where would I be without Paul's online notes? http://tutorial.math.lamar.edu/Classes/DE/UndeterminedCoefficients.aspx In example 3 he does what I would have guessed y_p=Asin(2t) but then he goes on to explain why that guess is flawed. something that @experimentX and @TuringTest have been trying to explain to me all along :S Thank's guys :)
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.2
sorry .. went offline :(
 2 years ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.