### Author Topic: MT Problem 4  (Read 4405 times)

#### Victor Ivrii

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##### MT Problem 4
« on: October 29, 2014, 09:00:48 PM »
Find Wronskian  $\ W(y_1,y_2,y_3)(x)\$ of a fundamental set of solutions  $\ y_1(x)\ ,\ y_2(x)\ ,\ y_3(x)\$ without finding the $\ y_j(x)$  ($j=1,2,3$) and then the general solution of the ODE
\begin{equation*}
(2-t)y''' + (2t-3) y'' -t y' + y = 0\ ,\ t < 2\ .
\end{equation*}
Hint: $\ e^t\$ solves the ODE.

#### Tanyu Yang

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##### Re: MT Problem 4
« Reply #1 on: November 04, 2014, 12:29:38 AM »
am I right?

#### Victor Ivrii

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##### Re: MT Problem 4
« Reply #2 on: November 04, 2014, 06:17:53 AM »
Yes. But it is too late: official solutions are in handouts

#### Tanyu Yang

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##### Re: MT Problem 4
« Reply #3 on: November 04, 2014, 01:16:16 PM »
Yes. But it is too late: official solutions are in handouts
Oops, I didn't know that lol.

#### Li

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##### Re: MT Problem 4
« Reply #4 on: November 19, 2014, 11:19:43 AM »
but t <2, how can I get ln(t-2) ?

#### Victor Ivrii

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##### Re: MT Problem 4
« Reply #5 on: November 19, 2014, 11:23:46 AM »
but t <2, how can I get ln(t-2) ?

You can get $\ln (2-t)$