Question

@ganeshie8 can you help me on the last part of the ques?

Answer 1

can you write out the steps for me please(:

Answer 2

familiar with solving the differential equation using separation of variables ?

Answer 3

\[\dfrac{dy}{dx} = \dfrac{xy}{3}\]

this can be rewritten as
\[\dfrac{1}{y}dy = \dfrac{x}{3}dx\]

Answer 4

integrate now

Answer 5

\[\int \dfrac{1}{y}dy = \int \dfrac{x}{3}dx\]

Answer 6

can you finish the rest ?

Answer 7

so which part is the problem..?

Answer 8

@perl can you please help? ganeshie left

Answer 9

did you get up to the integral part

Answer 10

its number 3, i just dont get what to do next

Answer 11

yeah i get it till he left

Answer 12

when we integrate we get
ln|y| = 1/3* x^2/2 + c

Answer 13

ohh and then what?

Answer 14

then we can raise both sides to the power of e

Answer 15

y = e^(x^2/6 + C)

do you agree so far?

Answer 16

yes! so we dont solve for c?

Answer 17

we will, but first I want to simplify the equation

Answer 18

okk

Answer 19

ln|y| = 1/3* x^2/2 + C
e^ln(y) = e^ ( x^2/6 + C )
y = e^(x^2/6 + C)

by law of exponents a^(m+n) = a^m * a^n

y = e^(x^2/6) * e^C



now bring the e^C in front, call it C again, since e^ constant = constant

Answer 20

that gives us the simplified version

y = C * e^(x^2/6)

Answer 21

and thats it?

Answer 22

thank you!(:

Answer 23

now plug in f(0) = 4

Answer 24

oh hahaha

Answer 25

4 = C * e^( 0^2/6)
4 = C * e^0
4 = C * 1

Answer 26

and just to be on the safe side, we can confirm with wolfram
http://www.wolframalpha.com/input/?i=solve+dy%2Fdx+%3D+xy%2F3+%2C+y%280%29%3D4

Answer 27

by the way, can someone tell me why we drop the absolute value bars
e^ln|y| becomes y