Toronto Math Forum

MAT244-2014F => MAT244 Math--Tests => MT => Topic started by: Victor Ivrii on October 29, 2014, 09:00:48 PM

Title: MT Problem 4
Post by: Victor Ivrii 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.

Title: Re: MT Problem 4
Post by: Tanyu Yang on November 04, 2014, 12:29:38 AM

am I right?

Title: Re: MT Problem 4
Post by: Victor Ivrii on November 04, 2014, 06:17:53 AM

Yes. But it is too late: official solutions are in handouts

Title: Re: MT Problem 4
Post by: Tanyu Yang on November 04, 2014, 01:16:16 PM

Quote from: Victor Ivrii on November 04, 2014, 06:17:53 AM

Yes. But it is too late: official solutions are in handouts

Oops, I didn't know that lol.

Title: Re: MT Problem 4
Post by: Li on November 19, 2014, 11:19:43 AM

but t <2, how can I get ln(t-2) ?

Title: Re: MT Problem 4
Post by: Victor Ivrii on November 19, 2014, 11:23:46 AM

Quote from: Li on November 19, 2014, 11:19:43 AM

but t <2, how can I get ln(t-2) ?

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