So for these types of questions (DE, undetermined coefficients), are you just expected to use the product rule 60...

I'm more concerned that you're, supposedly, a math major that has never studied the theory of neither ODES nor PDES, I can only assume that your actually just a first (maybe second) year undergrad or your schooling was particularly poor.

A lot of phenomena in nature are described by DEs. Really though all the good ones have to be solved numerically anyway.

Nah. Graduating this December, Ivy League university.

Learned about ODEs in high school from a friend. I don't really understand how they dedicate an entire class to what seemed like such a small amount of material. But then I read a book on applied PDEs and, not including the research level PDEs that involve analysis and such, it wasn't so bad.

Just seems like applied math, and there's nothing wrong with applied math, but rote computations don't really interest me.

wow your so smart

Stop complaining OP. That particular equation perfectly models the wave of shitposting across boards when a shitpost of magnitude 2.0 is posted with a new meme.

You should have learned at least the Peano and the Picard-Lindelöf theorem concerning existence and uniqueness of solutions of IVP for ODEs. Also a little theory on extensibility of solutions and bifurcation theory.

While PDEs are not standard, the field is much more broad, and theory of existence and uniqueness is extremely complex.

>take Laplace transform of every ode I run into
>do algebra instead of calculus
>disregard math majors who want to stick their heads so far up their asses they turn into a Klein bottle

pedophile scum

>math major
>didn't study ODEs or PDEs
ok bro

m8 that's only a second order DE. You should practice that shit until you can do it in your sleep. What's your major?

>What's your major?
biology, why?

Kill yourself

>topology
>algebraic topology
>no ODE/PDE background

le autistic pure math face

Ah ok, I don't know how prevalent they are in biology but I imagine they are pretty useful there as well. It might be a pain in the arse to do these questions but it's all good practise, just like doing push ups or taking a run. You want to be able to do these with your eyes closed when it's just a small part of a larger problem. The worst thing is to get caught up on the maths when you really want to be thinking about the science.

You use odes in population models.
It's used to determine how many of a species can be harvested, for example.

You can also use it to study the behavior of vaccinations, or dissemination of a chemical in your blood stream.

Almost everything in the real world is modeled using odes

It's almost as if different people have different academic interests.

kek

intro to ODEs class is mandatory for a math bachelor at my university, PDE isn't.
Even though our ODE classes are lot more theoretical, than what most people on Veeky Forums would consider an ODE class. The lecture didn't even cover any solution methods, which were only in the exercises.
I would consider differential equations applied math, but it's a topic far from rote computation if you do it on a math level and not a physicist's/engineer's.
There's a lot of theory that heavily relies on functional analysis and general operator theory.
For example if you look at stuff like heat transfer, you have a PDE like
[math] u_t = \Delta u [/math]
but you can also analyse it like a linear ODE in a banach space setting
[math] u_t = A u [/math]
ODE theory would tell us, that the solution is [math] u = exp(At) [/math], but to actually make sense of an expression like [math] exp(\Delta t) [/math] you would need to go deep into functional analysis

AUTIST