Is anybody in here smart enough to solve this?

# Is anybody in here smart enough to solve this?

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.

y=2, t=1.

Any other questions?

LOL

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

fuck you

differential equations

what are you, a college junior?

You are.

I believe in you OP

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

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

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

I'm super smart

lol

anyone who says this unironically is 100% a fucking brainlet

I'm super smart

sure buddy

got a 3

3 on what scale

then pls tell us what the correct solution was, it's already been posted here.

Let's see who the brainlet is

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

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

being this much of a brainlet

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...

percentile

First order linear ODE?

I could do that in high school.

Integrating factors are for babies.

Then apologies, my gentleman

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

yes there are many of us

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

user, isn't a stupid answer, try actually reading it

[math]

3y' + 6ty = 12 \\

3\dfrac{dy}{dt} + 6ty = 12 \\

y=4t \\

\dfrac{dy}{dt} = 4\\

t=0

[/math]

autism

so many retards...

At least this guy knows how to enter it into wolfram

Uh its already solved, tardcart

what is the function y(t) then, faggot

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.

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

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).

isn't a stupid answer

second line is wrong