Bill Goodwine's Courses

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?

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?

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.

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?

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.

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.

If a/c<0 then it must be true that c/a<0.