## Homework 2, due September 8, 2004

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

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
• 2. Determine the solution to
• 3. Determine the general solution to
• 4. Determine the solution to
• 5. Determine the solution to
• 6. Determine the general solution to
• 7. Determine the solution to
• 8. Determine the general solution to
• 9. Determine the general solution to
• 10. Determine the solution to
• 11. Determine the solution to
• 12. Determine the general solution to
• Last edited by goodwine on Thu Jun 15, 2006 4:43 pm, edited 4 times in total.
goodwine
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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.
• • • • • • • • 1. Oops. There should be a + between the c1 and c2 terms.
• 2. Updated at 10:00am, Friday September 3.
• Last edited by goodwine on Thu Jun 15, 2006 4:43 pm, edited 4 times in total.
Bill Goodwine, 376 Fitzpatrick
goodwine
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### Re: answer 10...

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
goodwine
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### Re: answer 10...

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

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

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

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

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.
goodwine
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### Re: Solution 1

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
Is answer #5 correct. I get: 11*exp(t/2) + 10*exp(t/3)
Grendel
For answer #3, I get: 15*exp(3*t) - t*exp(2*t) - 2/3*exp(2*t) + 14*exp(-t)[/b]
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

correction, i get 1/4 and 3/4. but this is still different from your answer.
goodwine
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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.
Bill Goodwine, 376 Fitzpatrick
goodwine
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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.
Bill Goodwine, 376 Fitzpatrick
goodwine
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### Re: answer #3

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

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

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

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?
goodwine
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### Re: Problem 7

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

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?
goodwine
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### Re: number 3

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

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