Toronto Math Forum
MAT2442018F => MAT244Lectures & Home Assignments => Topic started by: Daniel Clark on October 12, 2018, 03:43:18 PM

So I had this idea of putting all of the lecture material of MAT244 in a giant flowchart. So I did.
A few notes:
Dotted lines means the question is reduced to the smaller one
For the partial derivatives I used notation not used in class, the curly "d" with a subscript just means a derivative with respect to the variable in the subscript
I tried to keep it on one page and have all the notation as general as possible, which might have made it nigh impossible to read. Sorry about that.
I don't have EVERYTHING, and I'm planning to update it as the class goes on. Constrictive criticism welcome.

Wowzers!!!
But you forgot in integrating factor case of $\mu= \mu (xy)$.
And somehow relevant
https://www.nytimes.com/2010/04/27/world/27powerpoint.html?hp (https://www.nytimes.com/2010/04/27/world/27powerpoint.html?hp)

I think that if you had a nonexact homogeneous equation and you can't easily find an integrating factor, you could also solve it by making a substitution y=vx.. then it would be reduced to a separable equation.

RE: Kathryn Bucci
Incorrect, counterexample x +(x^2y^2)y' = 0
using the substitution gives us x +(x^2v^2x^2)v' =0 which is arguably worse.
That would work if the derivative is a function of the ratio, which i covered in my unholy diagram on the left.

Daniel, Kathryn
The word "homogeneous" is overused. Kathryn is right if equation is homogeneous which means $y'=f(y/x)$. Daniel meanwhile thinks about linear homogeneous, which is a completely different story.

Daniel, Kathryn
The word "homogeneous" is overused. Kathryn is right if equation is homogeneous which means $y'=f(y/x)$. Daniel meanwhile thinks about linear homogeneous, which is a completely different story.
Yes that is what I was referring to  sorry, I should have been more clear.