Question

given y>0 and dy/dx=3x^2+4x/y. if the point (1,sqrt{10}) is on the graph relating x and y, then what is y when x=0?

Answer 1

no chance that's supposed to be
dy/dx=(3x^2+4x)/y
is it ?

Answer 2

it is

Answer 3

he didn't like my answer
maybe you can try turing

Answer 4

Ah, I see...
You should trust myininaya spikey

Answer 5

lol i didnt understand it :(

Answer 6

but no he might understand you better

Answer 7

http://openstudy.com/study#/updates/4f1ccb76e4b04992dd23dbf3

Answer 8

dy/dx=(3x^2+4x)/y yes thats correct

Answer 9

this is what i did turing if you want to look

Answer 10

yep thats the other one :) do you wanna work off here or of the other one.

Answer 11

ok...
this is a very basic separation of variables problem, in which we can treat dy/dx like a regular fraction...
dy/dx=(3x^2+4x)/y
ydy=3x^2+4xdx
now integrate both sides...
but according to the other post you don't seem to know how integrate yet :/

Answer 12

you don't know how to integrate that*
correct?

Answer 13

hmm im not sure. if you mean using anti derivaties than sort of

Answer 14

\[\int\limits_{?}^{?}\] but i havent used this yet

Answer 15

yes exactly antiderivatives

Answer 16

\[\int\limits_{}^{}x^n dx=\frac{x^{n+1}}{n+1}+C, n \neq -1\]

Answer 17

or you could say the antiderivative of x^n = that

Answer 18

ahh yes that sort of makes sense.

Answer 19

i understand that c is a constant.

Answer 20

check that the derivative of that gives x^n

Answer 21

right

Answer 22

the derivative of ydy=(3x^2+4x)dx?

Answer 23

antiderivative of that

Answer 24

no we want to integrate both sides
or we can use the term antiderivative

Answer 25

like turing said

Answer 26

ahh okay.

Answer 27

so what is the antiderivative of
ydy
according to the formula myin posted?

Answer 28

x^3

Answer 29

for 3x^2

Answer 30

i dont know for 4x

Answer 31

yes
but that is not ydy...
like I said, I can't use latex, myin will have to show you

Answer 32

\[\int\limits_{}^{}y dy =\int\limits_{}^{}y^1 dy=\frac{y^{1+1}}{1+1}+c_1\]

Answer 33

see n was 1 here

Answer 34

okay im struggling alot right now because i havent had enough practice with this.

Answer 35

its cool

Answer 36

struggling happens
but the main is don't give up

Answer 37

okay so the rule is for 3x^2 x^n+1

Answer 38

what formula for the 4x?

Answer 39

the anti derivative of dx is x?

Answer 40

4x=4x^(1)
so we can use the same formula
integral of
(x^n)dx=x^(n+1)/(n+1)

Answer 41

\[\int\limits_{}^{}3x^2 dx=3 \int\limits_{}^{}x^2 dx=3 \cdot \frac{x^{2+1}}{2+1}+c_2\]

Answer 42

\[\int\limits_{}^{}4x dx=4 \int\limits_{}^{}x dx=4\int\limits_{}^{}x^1 dx=4 \cdot \frac{x^{1+1}}{1+1}+c_3\]

Answer 43

see i'm using that same formula every time

Answer 44

oh okay so i have to do it for each.

Answer 45

right

Answer 46

\[\int\limits_{}^{}(f(x)+g(x))dx=\int\limits_{}^{}f(x) dx+\int\limits_{}^{}g(x)dx\]

Answer 47

so we have
\[\frac{y^2}{2}+c_1=3 \cdot \frac{x^{2+1}}{2+1}+c_2+4 \cdot \frac{x^{1+1}}{1+1}+c_3\]

Answer 48

so for the formula ydy you used the formula.

Answer 49

okay i understand how u got that equation.

Answer 50

or you could write instead
\[\frac{y^2}{2}=3 \cdot \frac{x^{2+1}}{2+1}+4 \cdot \frac{x^{1+1}}{1+1}+C\]
since the sum of some constants is still a constant

Answer 51

yes

Answer 52

ok great! lets make this prettier

Answer 53

\[\frac{y^2}{2}=x^3+2 x^2+C\]

Answer 54

is that okay?

Answer 55

yes my simplification came out the same

Answer 56

ok we can also multiply two on both sides

Answer 57

\[y^2=2x^3+4x^2+C\]

Answer 58

2C is still constant so I left it as C

Answer 59

yes

Answer 60

you can write 2C if you feel more comfortable with that

Answer 61

and now square both sides?

Answer 62

square root of both sides

Answer 63

we don't need to keep the negative value since your directions say y>0

Answer 64

where do we have a negative value?

Answer 65

take square root of both sides
you get plus or minus

Answer 66

thats right!

Answer 67

we only need the plus since y>0

Answer 68

so what I'm saying is that we have
\[y=\sqrt{2x^3+4x^2+C}\]

Answer 69

yes.

Answer 70

you were given a point on this curve

Answer 71

\[ (1,\sqrt{10} )\]

Answer 72

x=1 and y=sqrt(10)

Answer 73

yes i plug it in for x and y?

Answer 74

so we can use this to find C

Answer 75

\[\sqrt{10}=\sqrt{2 (1)^3+4(1)^2+C}\]
=>
\[10=2(1)^3+4(1)^2+C\]

Answer 76

\[10=2+4+C\]

Answer 77

=>C=4

Answer 78

so we have
\[y=\sqrt{2x^3+4x^2+4} \]

Answer 79

you wanted to know y when x=0, right?

Answer 80

yes

Answer 81

so how do you think we do that?

Answer 82

i brb
i think it will be pretty easy for turing to help without latex on this last part that you have to do

Answer 83

okay turing i get now :D

Answer 84

but i need help finishing

Answer 85

ok i'm back

Answer 86

i had to get my glasses

Answer 87

so i can be fully nerd

Answer 88

lol

Answer 89

so we have \[y=\sqrt{2x^3+4x^2+4}\]

Answer 90

yes

Answer 91

it says what is y if x=0

Answer 92

\[y=\sqrt{2(0)^3+4(0)^2+4}\]

Answer 93

i replaced x with 0 so I can see what y is when x is 0

Answer 94

\[y=\sqrt{0+0+4}=\sqrt{4}=2\]

Answer 95

This says when x is 0, y is 2

Answer 96

got it! :D thank you!!!! sorry i didnt really try hard enough before you were a great help!

Answer 97

It is okay. I didn't think any offense to anything you did. Sometimes you may get someone who can explain it better. I know that I'm probably not the best explaining some things.

Answer 98

Or you know like I way you prefer.