Homework 2, due September 8, 2004

Due Wednesday, September 8, 2004. Grader: Michaela Logue (Logue.3@nd.edu)
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goodwine
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Homework 2, due September 8, 2004

Post by goodwine »

Solve each of the following differential equations using the methods from chapters 2 and 3 in the course text. If the equation cannot be solved using a method from chapters 2 or 3 in the course text, the correct answer is to indicate that the equation cannot be solved using the methods from the course text.

Note: this homework is longer than what will be typical for this course.

Each problem is worth 10 points.
  1. Determine the solution to
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  2. Determine the solution to
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  3. Determine the general solution to
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  4. Determine the solution to
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  5. Determine the solution to
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  6. Determine the general solution to
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  7. Determine the solution to
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  8. Determine the general solution to
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  9. Determine the general solution to
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  10. Determine the solution to
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  11. Determine the solution to
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  12. Determine the general solution to
    • Image
Last edited by goodwine on Thu Jun 15, 2006 4:43 pm, edited 4 times in total.
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Some answers

Post by goodwine »

Here are the answers to the problems that can be solved using the book methods. They are not in the same order as the assigned problems.
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  1. Oops. There should be a + between the c1 and c2 terms.
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  2. Updated at 10:00am, Friday September 3.
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Last edited by goodwine on Thu Jun 15, 2006 4:43 pm, edited 4 times in total.
Bill Goodwine, 376 Fitzpatrick
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Re: answer 10...

Post by goodwine »

lisaturtle wrote:if answer 10 is a solution to the problem i think it is, then it should be e^(-t). i tried using that answer as the solution to the problem i was working on and found that it actually wasn't a solution. is this right, or am i doing the problem wrong?
I'll check in the morning. If you're pretty sure about the e^(-t) then I probably just typed the answer incorrectly.
Bill Goodwine, 376 Fitzpatrick
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Re: answer 10...

Post by goodwine »

goodwine wrote:
lisaturtle wrote:if answer 10 is a solution to the problem i think it is, then it should be e^(-t). i tried using that answer as the solution to the problem i was working on and found that it actually wasn't a solution. is this right, or am i doing the problem wrong?
I'll check in the morning. If you're pretty sure about the e^(-t) then I probably just typed the answer incorrectly.
I typed the original problem incorrectly (it should have been e^(-t) instead of e^(t)). Anyway, the answer is now correct. There was also an error in the (1-t) term.
Bill Goodwine, 376 Fitzpatrick
The Kid

solution number 8

Post by The Kid »

in solution #8 i got the last 1 to be 13, i just wanted to see if i did something wrong.
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Re: solution number 8

Post by goodwine »

The Kid wrote:in solution #8 i got the last 1 to be 13, i just wanted to see if i did something wrong.
I get a 1. If a bunch of other people get 13, then I may be wrong, but I don't think so.
Bill Goodwine, 376 Fitzpatrick
NDChevy07

Re: solution number 8

Post by NDChevy07 »

goodwine wrote:
The Kid wrote:in solution #8 i got the last 1 to be 13, i just wanted to see if i did something wrong.
I get a 1. If a bunch of other people get 13, then I may be wrong, but I don't think so.

I got a 1, too. I'd just check your addition. With the fractions it can get messed up easily.
NDChevy07

Solution 1

Post by NDChevy07 »

I got the last three terms in solution 1, but where do the sin/cos terms come from. I tried plugging them in as undetermined coefficients to solve them to equal zero, but I got mixed up.
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Re: Solution 1

Post by goodwine »

NDChevy07 wrote:I got the last three terms in solution 1, but where do the sin/cos terms come from. I tried plugging them in as undetermined coefficients to solve them to equal zero, but I got mixed up.
I suspect you are forgetting the homogeneous solution.
Bill Goodwine, 376 Fitzpatrick
Grendel

Post by Grendel »

Is answer #5 correct. I get: 11*exp(t/2) + 10*exp(t/3)
Grendel

Post by Grendel »

For answer #3, I get: 15*exp(3*t) - t*exp(2*t) - 2/3*exp(2*t) + 14*exp(-t)[/b]
nwohrle

answer #3

Post by nwohrle »

for answer #3, the exponents for the 1st and 2nd term are 1 and 2/3 respectively. I get 3/4 and 1/4. this is for the homogeneous solution. what am i doing wrong?
nwohrle

correction

Post by nwohrle »

correction, i get 1/4 and 3/4. but this is still different from your answer.
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Post by goodwine »

Justin Case wrote:For answer #3, I get: 15*exp(3*t) - t*exp(2*t) - 2/3*exp(2*t) + 14*exp(-t)[/b]
I just checked again. I think #3 is right.
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Post by goodwine »

Justin Case wrote:Is answer #5 correct. I get: 11*exp(t/2) + 10*exp(t/3)
I checked again. I get the same as is posted for #5.
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Re: answer #3

Post by goodwine »

nwohrle wrote:for answer #3, the exponents for the 1st and 2nd term are 1 and 2/3 respectively. I get 3/4 and 1/4. this is for the homogeneous solution. what am i doing wrong?
I still get the same coefficients are are posted for #3. I'd double-check your math unless someone else contradicts me.
Bill Goodwine, 376 Fitzpatrick
NDChevy07

Two unsolvable problems

Post by NDChevy07 »

What do we do with the two problems that don't have solutions? Do we solve them numerically, or just say they can't be solved?
maniacmechanix

Unsolvable ones

Post by maniacmechanix »

He said at the top of the homework to just state they are not solvable using the methods in chapters 2 and 3.
PhillyPhan17

Problem 7

Post by PhillyPhan17 »

To solve problem 7 i used the method of undetermined coefficients....
i used the following formula: x(t) = (At + B)*exp(2*t)

I was able to solve the equation and satisfy the initial conditions but my solution looks nothing like the one posted....is there anything i'm doing wrong?
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Re: Problem 7

Post by goodwine »

PhillyPhan17 wrote:To solve problem 7 i used the method of undetermined coefficients....
i used the following formula: x(t) = (At + B)*exp(2*t)

I was able to solve the equation and satisfy the initial conditions but my solution looks nothing like the one posted....is there anything i'm doing wrong?
That is the right approach and you assumed the correct form for the right hand side. You must have made an error determining the homogeneous solution or an algebra error in the computation of A and B. Either that or maybe you are comparing it with an answer that goes with another problem.
Bill Goodwine, 376 Fitzpatrick
iluvpnutbtr

number 3

Post by iluvpnutbtr »

For number three I am using integrating factor, but I can't seem to intigrate 1/(t(ln(t)-2)). What am i doing wrong?
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Re: number 3

Post by goodwine »

iluvpnutbtr wrote:For number three I am using integrating factor, but I can't seem to intigrate 1/(t(ln(t)-2)). What am i doing wrong?
I didn't even notice the equation was linear. It turns out that the computations are easier if you check if it is exact and proceed from there.
Bill Goodwine, 376 Fitzpatrick
nwohrle

answer # 1

Post by nwohrle »

shouldn't the first variable for answer #1 should be 7/20.
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Re: answer # 1

Post by goodwine »

nwohrle wrote:shouldn't the first variable for answer #1 should be 7/20.
I'm pretty sure that answer #1 is correct. Of the 20 or so people that came to my office hours, no one questioned that answer.
Bill Goodwine, 376 Fitzpatrick
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