Toronto Math Forum
Welcome,
Guest
. Please
login
or
register
.
1 Hour
1 Day
1 Week
1 Month
Forever
Login with username, password and session length
News:
Home
Help
Search
Calendar
Login
Register
Toronto Math Forum
»
MAT244-2013S
»
MAT244 Math--Lectures
»
Ch 1--2
»
Bonus problem of the week 1:
« previous
next »
Print
Pages: [
1
]
Author
Topic: Bonus problem of the week 1: (Read 5063 times)
Victor Ivrii
Administrator
Elder Member
Posts: 2563
Karma: 0
Bonus problem of the week 1:
«
on:
January 10, 2013, 07:34:59 AM »
Submitting (first) the correct solution of the "Problem of the Week" (I will try to post them each week) you get karma which translates to bonus marks.
(a) Find the
general solution
of
\begin{equation}
x y'= 2 y(4-y)
\label{eq-1}
\end{equation}
(b) Find solution of (\ref{eq-1}) (as $x>0$) satisfying
initial condition
$y(1)=1$;
(c) Using computer f.e.
http://math.rice.edu/~dfield/dfpp.html
solve (a), (b) graphically: output will two pictures: each containing a field of directions and several integral lines in (a), and one particular line in (b).
Logged
Felipe Morgado
Newbie
Posts: 1
Karma: 1
Re: Bonus problem of the week 1:
«
Reply #1 on:
January 10, 2013, 09:43:59 AM »
It looks like this can be solved by separation. Hopefully this is right (the first graph shows several integral curves for (a), and the second shows the particular solution specified in (b)).
Logged
Victor Ivrii
Administrator
Elder Member
Posts: 2563
Karma: 0
Re: Bonus problem of the week 1:
«
Reply #2 on:
January 10, 2013, 11:13:10 AM »
OK. Sure I prefer it be typed than scanned but your scan is good.
Logged
Print
Pages: [
1
]
« previous
next »
Toronto Math Forum
»
MAT244-2013S
»
MAT244 Math--Lectures
»
Ch 1--2
»
Bonus problem of the week 1: