Question

\[y'+3x^2y=x^2\]

Answer 1

\[y'+\color{red}{3x^2}y=x^2\] we start by finding \(\mu\) in two steps

Answer 2

take the function of x in from of the y and integrate it wrt x

Answer 3

\[\int 3x^2dx\] is step 1

Answer 4

So x^3

Answer 5

right

Answer 6

next step, raise \(e\) to that power, that is your \(\mu\)

Answer 7

e^(x^3))

Answer 8

that is \(\mu\) now multiply both sides by your \(\mu\) and you will have, on the left, the derivative of \(\mu u\)

Answer 9

i mean the derivative of \(\mu y\)

Answer 10

e^(x^3))*y' + e^(2x^3)) = e^(x^3))*(x^2)

Answer 11

yes, and integrating on the left gives \[e^{3x}y\] so your only real job is to integrate on the right

Answer 12

So u-sub?

Answer 13

yes mental u sub

Answer 14

(1/3)e^(x^3)

Answer 15

I don't think thats right

Answer 16

i do

Answer 17

plus c, which is kind of important

Answer 18

Shouldn't the x come out front?

Answer 19

god help me

Answer 20

you were right, leave it be

Answer 21

Ok

Answer 22

\[e^{3x}y=\frac{1}{3}e^{3x}+c\] the c is real important

Answer 23

Okie

Answer 24

gives \[e=\frac{1}{3}\] but with it you get \[y=\frac{1}{3}+ce^{-3x}\]

Answer 25

that didnt come out right at all

Answer 26

Nope

Answer 27

i meant if you forget the c and solve for y you get \[y=\frac{1}{3}\]

Answer 28

but the correct answer is \[y=\frac{1}{3}+ce^{-3x}\]

Answer 29

Right

Answer 30

why this miracle works is explained on page 55
i have time for one more if you like, just so you get the hang of it

Answer 31

I appreciate it but I'm so tired. Tomorrow?

Answer 32

ok you try some though
method is probably not clear yet but we did all the steps to find mu

Answer 33

I will do 2.3 tomorrow.

Answer 34

I should come annoy you Saturday or something

Answer 35

ok that is this section, do a ton
i am not free saturday
birthday party for a 3 year old

Answer 36

is your job monday through friday?

Answer 37

I will do my entire assigned homework problems. And well maybe a weekend soon. My exam is on the 27th of June so I have to annoy you sometime about it. (if you're free of course)

Answer 38

And yes it is. I come back to philly on the weekends

Answer 39

ok we will see
we can do some tomorrow night if you like, send me a text

Answer 40

g'night

Answer 41

Absolutely

Answer 42

Thank you! Goodnight!