Homework 4 solutions

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Homework 4 solutions
Bill Goodwine, 376 Fitzpatrick
Exam 1
Professor Goodwine,
I am having some trouble on the first question of exam 1 for Fall 2015. From the look of the equation for question 1, it is nonlinear and therefore can only be solved as an exact equation of a separable equation. I feel that the method to solve would be separable, but when attempting to integrate I ended up with an integral that was intensive and resulted in a tanh. Am I going about this problem the wrong way?
I am having some trouble on the first question of exam 1 for Fall 2015. From the look of the equation for question 1, it is nonlinear and therefore can only be solved as an exact equation of a separable equation. I feel that the method to solve would be separable, but when attempting to integrate I ended up with an integral that was intensive and resulted in a tanh. Am I going about this problem the wrong way?

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Re: Exam 1
As I recall that is correct. I announced during the exam if you ended up with an integral you couldn't evaluate that you would receive most of the credit.smayers wrote:Professor Goodwine,
I am having some trouble on the first question of exam 1 for Fall 2015. From the look of the equation for question 1, it is nonlinear and therefore can only be solved as an exact equation of a separable equation. I feel that the method to solve would be separable, but when attempting to integrate I ended up with an integral that was intensive and resulted in a tanh. Am I going about this problem the wrong way?
Bill Goodwine, 376 Fitzpatrick
Re: Homework 4 solutions
For the homework 4 solutions, 3.10, the legend calls out c1=1 and c2=2 for all 4 curves and they're all in the same color...which curve goes with which c1 and c2?
Re: Homework 4 solutions
For the homework 4 solutions, 3.12, the questions asks for a proof that the homogenous solution is unstable if b/a<0 or if c/a<0, but in the solutions the first part gives the solution for if b/a<1 and the second part gives the solution for if a/c<0. I don't understand the correlation between the inequalities given in the solution and the ones given in the question.

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Re: Homework 4 solutions
If a/c<0 then it must be true that c/a<0.bcorbin wrote:For the homework 4 solutions, 3.12, the questions asks for a proof that the homogenous solution is unstable if b/a<0 or if c/a<0, but in the solutions the first part gives the solution for if b/a<1 and the second part gives the solution for if a/c<0. I don't understand the correlation between the inequalities given in the solution and the ones given in the question.
Bill Goodwine, 376 Fitzpatrick