Messages

1291

TT1 / TT1-problem 3

« on: October 09, 2014, 02:00:15 AM »

Find the general solution for equation
\begin{equation*}
z''(t)-z'(t)-6z(t)=-6+10 e^{-2t} .
\end{equation*}

1292

TT1 / TT1-problem 2

« on: October 09, 2014, 01:59:21 AM »

a. Find Wronskian  $W(y_1,y_2)(x)$ of a fundamental set of solutions $y_1(x) , y_2(x)$ for ODE 
\begin{equation*}
x^3(\ln x+1)\cdot  y''(x) -(2\ln x+3)x^2 \cdot y'(x) + (2\ln x+3) x y(x) = 0,\qquad
x>1.
\end{equation*}

b. Check that $y_1(x)=x$ is a solution and find another linearly independent solution.

1293

TT1 / TT1-problem 1

« on: October 09, 2014, 01:57:52 AM »

Find integrating factor and then a general solution of ODE
\begin{equation*}
y + (2xy - e^{-2y})y' = 0 \ .
\end{equation*}
Also, find a solution satisfying $y(1)=-2$ .

1294

Quiz 2 / Re: Quiz 2 Problem 2 (night sections)

« on: October 02, 2014, 04:07:52 AM »

A bit simpler: the general solution is $y=\bigl(C_1 + C_2 (t+1)\bigr) e^{-2 (t+1)}$: it is equivalent (with the different constants to $\bigl(C_1 + C_2 t\bigr) e^{-2 t}$ but we simply moved the "time" to start from $0$ rather than from $-1$: $t_{\text{new}}=t+1$.

Then $y(-1)=C_1=2$ and $y'(-1)= -2 C_1+ C_2=1$. Then $C_1=2$, $C_2=5$ and $y=(7+5t)e^{-2t+2}$. Indeed graph is similar to one sketched by Yeming Wen: it tends to $+0$ as $t\to +\infty$, crosses $y=0$ as $t=-7/5$ and fast tends to $-\infty$ as $t\to -\infty$.

1295

Quiz 2 / Re: Quiz 2 3.4 #14

« on: October 02, 2014, 01:38:07 AM »

Michael Boutros,
I wrote:

I plan to give intro to 2nd order equations and then to cover sections 3.1, 3.2 and may be start 3.3.

It was a plan, not the actual content. Instead, in L5101 we covered 3.1, 3.2 and 3.4 because 3.4 is much more simple and shorter,  than 3.3 and there was no point to start 3.3 after Quiz 1.

All other sections did the same. When students asked me to write what I am planning to do I warned that plans are always approximate. 

1296

Quiz 1 / Q1 problem 2 (day section)

« on: September 29, 2014, 02:21:44 AM »

Please post problem and solution

1297

Quiz 1 / Q1 problem 1 (day section)

« on: September 29, 2014, 02:21:19 AM »

Please post problem and solution

1298

Quiz 1 / Re: Q1 problem 2 (Night sections)

« on: September 26, 2014, 09:54:32 PM »

I dont use intergrating factor for this problem, instead I use an alternative  approach

It is difficult to decrypt. Please rewrite (quote one of the previous posts to see how to display math properly), check spelling and fix your name

1299

WebWorks / Re: WW2-problem 6

« on: September 25, 2014, 02:33:25 AM »

This is not a book's but a WebWork's issue. At the moment we just testing it. Any experience posted is appreciated. I am not sure if the system is smart enough to ignore superficial spaces

1300

Quiz 1 / Re: Q1 problem 1 (L5101)

« on: September 25, 2014, 02:12:34 AM »

Roro. I rewrote your solution using superior math typesetting by MathJax (Javascript LaTeX/MathML parser). Everyone can quote my solution to see how it is done. Also fix your name.

Eddie. You got a karma as an exception: no need to post inferior technically (screenshot) solution after superior (typed) and correct. You could export your solution to LaTeX and after minimal corrections post "typed" solution. However code would be ugly and difficult to edit.

For everyone in the future: red is mine!

1301

Quiz 1 / Q1 problem 2 (Night sections)

« on: September 24, 2014, 10:19:51 PM »

Please post solution

2.6 p. 102, # 25 Solve the initial value problem
\begin{equation*}
y'-2y=e^{2t},\qquad y(0)=2.
\end{equation*}

1302

Quiz 1 / Q1 problem 1 (L5102)

« on: September 24, 2014, 10:18:13 PM »

Please, post solution

2.6 p. 102, # 25
Solve
\begin{equation*}
(3x^2+2xy+y^3)+ (x^2+y^2)y'=0.
\end{equation*}


PS. Please do not post solution to the corrected problem! Consider only problem as formulated here

1303

Quiz 1 / Q1 problem 1 (L5101)

« on: September 24, 2014, 10:17:48 PM »

Please, post solution

2.6 p. 102, # 25
Solve
\begin{equation*}
(3x^2y+2xy+y^3)+ (x^2+y^2)y'=0.
\end{equation*}

1304

Technical Questions / Re: testing svg

« on: July 02, 2014, 07:36:10 PM »

1305

Technical Questions / testing pdf

« on: June 23, 2014, 05:15:33 AM »

This is pdf