News and Information for students enrolled in 21-260 Differential Equations at Carnegie Mellon University during the Spring 2007 Semester.
Monday, April 2, 2007
Assignment for Week #11
The assignment for Week #11 has been posted. You can find a link on the Schedule page of the Course Website.
9 comments:
Anonymous
said...
for problem 3.9.8a, i am not getting the one of the coefficients to work out...only one. for the coefficeitn of e^(-5t)sin(sqrt(73)t) term, i get the coefficient to be 383443/(100sqrt(73)) they have 7300 in the denominator in the book (if you pull the 1/153281 out in front of the whole solution). Am I correct or is the book?
The good thing about differential equations is that you can always check your answer by plugging it back into the equation. In a sense it's harder to find the solution than checking if it is a solution.
If you look at your answer you see that it breaks into two parts, the solution to the homogeneous equation and the particular solution. To check your answer just plug it back in and see if your numbers work. If they do, then you are right and the book is wrong ... unless you make a mistake when plugging it back in :)
I don't know, but for some reason the book has two complementary solution terms -- I find that one of the coefficients is zero and so there should only be a sine term. Maybe I'm doing something wrong...
OK, I now understand the difference. I don't want to get in trouble for giving too much away, but it has to do with _when_ you use the initial value conditions.
I think for the benefit of both you and the TA's (we have to grade this), I should finish chris' thought on the initial condition.
You have to plug in the initial conditions *after* you have the general form of the solution. e.g. if the homogeneous solution is c1u1(t) + c2u2(t) and up(t) is the particular solution, then you have to evaluate the initial conditions on the function
9 comments:
for problem 3.9.8a, i am not getting the one of the coefficients to work out...only one. for the coefficeitn of e^(-5t)sin(sqrt(73)t) term, i get the coefficient to be 383443/(100sqrt(73)) they have 7300 in the denominator in the book (if you pull the 1/153281 out in front of the whole solution). Am I correct or is the book?
i can confirm your answer, it appears to me the book has a mistake.
The good thing about differential equations is that you can always check your answer by plugging it back into the equation. In a sense it's harder to find the solution than checking if it is a solution.
If you look at your answer you see that it breaks into two parts, the solution to the homogeneous equation and the particular solution. To check your answer just plug it back in and see if your numbers work. If they do, then you are right and the book is wrong ... unless you make a mistake when plugging it back in :)
I don't know, but for some reason the book has two complementary solution terms -- I find that one of the coefficients is zero and so there should only be a sine term. Maybe I'm doing something wrong...
Mathematica also gets a complementary solution with only one term, so I imagine we are right and the book is wrong.
Hmm... I just plugged the equation into mathematica and it gets the same solution as the book. Maybe it isn't wrong.
Mathematica Soln here: http://aycu02.webshots.com/image/14801/2004345745696421074_rs.jpg
OK, I now understand the difference. I don't want to get in trouble for giving too much away, but it has to do with _when_ you use the initial value conditions.
I think for the benefit of both you and the TA's (we have to grade this), I should finish chris' thought on the initial condition.
You have to plug in the initial conditions *after* you have the general form of the solution. e.g. if the homogeneous solution is c1u1(t) + c2u2(t) and up(t) is the particular solution, then you have to evaluate the initial conditions on the function
u(t) = c1u1(t)+c2u2(t) + up(t)
which can make a whole lot of difference
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