Homework 2, due September 8, 2004

[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
   • 
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
    • 

[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.

1. • 
2. • 
3. • 
4. • 
5. • 
6. • 
7. • 
8. • 
9. Oops. There should be a + between the c1 and c2 terms.
   • 
10. Updated at 10:00am, Friday September 3.
    • 

[goodwine]

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.

[goodwine]

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.

[The Kid]

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

[goodwine]

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.

[NDChevy07]

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]

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]

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.

[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, i get 1/4 and 3/4. but this is still different from your answer.

[goodwine]

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.

[goodwine]

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.

[goodwine]

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.

[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]

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

[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?

[goodwine]

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.

[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?

[goodwine]

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.

[nwohrle]

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

[goodwine]

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.