Is this shit supposed to be intuitive? Am I just forever brainlet?

Is this shit supposed to be intuitive? Am I just forever brainlet?

That question IS supposed intuitive.

But slope fields as a whole: are they supposed to be intuitive? Something I can look at and just "see"? Because I'm just not getting it outside of plugging in test points

is a parabola intuitive? no, but work with one enough times and it will be
same for this, really

maybe a parabola is pretty intuitive even to someone who didn't take precalculus, but you get the idea
maybe a better example would have been derivatives themselves

What do you know? Have you seen linearizstion? Show the other options.

>Show the other options
But the correct option is already there.

A good way to get intuition is by elimination, more when is mostly cualitative aspects. That is, understanding why can't the other options be truw without solving the diferential equation.

That part I get and can do fine. It seems like I'm supposed to be able to recognize the pattern based on a cursory look at the equation though (sort of like recognizing the correct polynomial curve based on looking at the eq rather than plugging in points). Is this not realistic?

You will be able to do it in time, I take it you’re getting introduced to diff equations right?

Started self study like a week ago in preparation for my first class on it this term. So far doing KA/MITOpencourseware/Lamar has been smooth sailing, so I feel like I must be missing something

A field assigns an object to every point in a space. A vector field assigns a vector; a scalar field assigns a scalar.

A slope field assigns a slope.

The answer to a differential equation is a function.

in this case every point has a slope assigned to it.

Since dy/dx = - x/y, you separate varables and integrate. y dy = - x dx, the integral of which is

y=-x plus some constant.

So the first example the field at every point is the negative slope represented by a small line segment showing the slope....

What app is that? Thanks.

Just the Khan Academy app. I know sci considers it brainlet tier, but it's helpful for calc, diff eq, and linear algebra

When I did my course on slope and vector fields, we mainly analysed their shapes and behaviours analytically. Memorisation of these wasn’t required, but you do learn just through experience some basic patterns like ellipses and exponentials to name a couple.

>literally basic shapes
>hurr durr how can i intuiditve
yea you're a brainlet sorry man :/ sux for you
Its literally right in front of you like, its visual, its circles, its really simple

retard

I get how everything corresponds. I'm wondering if I should be able to intuit the correct slope field from looking at the equation once, rather than plugging in points and checking against provided answers

WHOA WHOA WHOA.

You intigrate both sides... so, It's

y^2 = - x^2 +c

and then you're going to take a square root of a negative?

i think 1, cuz graphs are like when it's with - it's like \ and if its + it's like /

[math] \frac{y^2}{2} = \frac{x^2}{2}+c[/math]*

fuck I forgot the negative sign
-

It's cool OP just relax.
You don't have to look at it right away and immediately know the field. You are just missing the tools of how to start thinking of intuitively.

For example try to think about some particular regions and what dy/dx looks like there. For example the x and y axis (i.e. when y, and x are zero respectively), or say the line y=+/-x, you should be able to get a quick idea for the behaviour of dy/dx in these regions, then you can start applying intuition to help interpolate the rest of the field.

Once you do enough things like this you'll build an even deeper intuition that is harder to articulate but might steer you down even quicker paths to understanding the behaviour of a field like this.

that's the same thing

Multiply both sides of the equation by 2???