Question

Diff eq question!!

Answer 1

It's in the section with numerical methods and such, but I don't know how to solve this first part.

\[y' = t + y -3, y(0) = 2\]

Show that the solution y = phi(t) = 2-t

Answer 2

This is a first order linear ODE,
we can solve this pretty easily using an integrating factor.
Have you learned about that?

Or are you using some numerical approximation methods like Euler or something?

Answer 3

Yeah we have learned that. I just realized it was first order and linear after a little bit of thought actually lol. It being in the numerical methods section must have freaked me out!

Answer 4

Haha :)

Answer 5

I'm not sure why they're calling it phi(t), that seems a little weird. :p

Answer 6

It's our book's method of showing it's the exact solution, as opposed to an estimate using numerical methods

Answer 7

Ah interesting :o