# Is anybody in here smart enough to solve this?

TreeEater

Is anybody in here smart enough to solve this?

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VisualMaster

I'm assuming y' is d(y)/dy. Nonetheless, you have 2 unknowns and 1 equation. This cannot be solved without another given linearly independent equation.

eGremlin

y=2, t=1.

Any other questions?

LOL

idontknow

y=1, t=2 is obviously the only correct answer

fuck you

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Methnerd

differential equations
what are you, a college junior?

Carnalpleasure

You are.

I believe in you OP

Sharpcharm

solution is y(t) = c_1 e^(-t^2) + 2 sqrt(π) e^(-t^2) erfi(t)
btw.
pls don't make yourself look retarded and ask me what erfi is

Flameblow

y' = 4 - 2ty
y = 4y + ty^2
1 = 4 + ty
-3 = ty
t = -3/y

y' + 2ty = 4
4 - 2ty + 2ty = 4

4 - 2y(-3/y) + 2y(-3/y) = 4

-2y(-3/y) + 2y(-3/y) = 0

6 - 6 = 0

what do i win

RumChicken

Wow it's almost like t is a variable not any random constant you make up

I'm actually a freshman LOL I'm super smart though I took AP calc in high school and got a 3 on the test

FastChef

I'm super smart
lol
anyone who says this unironically is 100% a fucking brainlet

CodeBuns

I'm super smart
sure buddy
got a 3
3 on what scale

Spazyfool

then pls tell us what the correct solution was, it's already been posted here.
Let's see who the brainlet is

Garbage Can Lid

AP exams are scored out of 5. 3 is literally brainlet tier.

Crazy_Nice

it's out of 5, 3 is just under 50%

farquit

being this much of a brainlet

5mileys

I hate this way of writing. If y is a function, and t is the variable, you should write
[math]\forall t, 3y'(t) + 6ty(t) = 12[/math]

You wouldn't have stupid answers as

But somehow mathematicians find this rigorous...

SniperGod

percentile

TechHater

First order linear ODE?
I could do that in high school.
Integrating factors are for babies.

BunnyJinx

Then apologies, my gentleman

whereismyname

no, anyone who knows differential equations would know what OP means. they are just retarded highschoolers who try to look smart.

Illusionz

yes there are many of us

Need_TLC

3 unknowns* (also y'). Also needs an initial condition (another lin indep equation).

Lord_Tryzalot

Supergrass

[math]
3y' + 6ty = 12 \\
3\dfrac{dy}{dt} + 6ty = 12 \\
y=4t \\
\dfrac{dy}{dt} = 4\\
t=0
[/math]

hairygrape

autism

Nojokur

so many retards...
At least this guy knows how to enter it into wolfram

Booteefool

SomethingNew

what is the function y(t) then, faggot

Spazyfool

how the fuck do you get a 3 on that exam

Not him but our school accidentally gave us the bc instead of the ab. Still passed lul.

King_Martha

didn't even know sequences and series other than how to do a taylor expansion and got a 5 on the BC exam
it was definitely the easiest AP test i took

5mileys

This is an embarrassing performance by all the anons posting before me.

In any case, here we have an inhomogeneous linear first order ODE. This would indicate that we should use an integrating factor. First, divide by 3:
y' + 2ty = 4
Then, we will try the integrating factor u(t) = e^(integral of 2t) = e^(t^2).
Multiplying through, we get
y'*e^(t^2) + y*2te^(t^2) = 4e^(t^2)
The left hand side is just
(y*e^(t^2))' = 4e^(t^2)
Now we integrate:
y*e^(t^2) + C = integral of 4e^(t^2) (which sadly has not got a closed form)
so if y is a solution, it must be of the form y = (C + integral of 4e^(t^2))*e^(-t^2)
Using initial conditions, C can be determined.
Then, you should plug the answer back in to show that y is indeed a solution (fuck doing that though).

PurpleCharger

second line is wrong