# Toronto Math Forum

## MAT244-2018S => MAT244--Tests => Term Test 1 => Topic started by: Victor Ivrii on February 13, 2018, 09:24:12 PM

Title: P-2
Post by: Victor Ivrii on February 13, 2018, 09:24:12 PM
(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*}
\bigl(x\sin(x)+\cos(x)\bigr)y''-x\cos(x)y'+\cos(x)y=0
\end{equation*}
(b) Check that $y_1(x)=x$ is a solution and find another linearly independent solution.

(c) Write the general solution,  and find solution such that ${y(0)=1, y'(0)=1}$.

Title: Re: P-2
Post by: Wanying Zhang on February 14, 2018, 10:17:53 AM
Solution to Problem 2:
Title: Re: P-2
Post by: Meng Wu on February 14, 2018, 10:22:08 AM
Solution to Problem 2:

Prof. Victor would prefer you typing out the solutions xD ( that is if you want the bonus mark)
Title: Re: P-2
Post by: Wanying Zhang on February 14, 2018, 10:25:22 AM
The last picture is hard to read, so I upload again. Sorry for that!
Title: Re: P-2
Post by: Wanying Zhang on February 14, 2018, 11:56:09 AM
I have trouble typing on the forum so I type it and convert to PDF form. Hope it better.
Title: Re: P-2
Post by: Victor Ivrii on February 14, 2018, 12:00:57 PM
You typed using LaTeX (which is fine, but you need to put escape character \ in front of mathoperators like \cos ....)

Then you can just copy and paste into forum your source and make minimal editing (use "preview" to see what needs to be corrected). When I post Quizzes and Tests problems to forum, I also do not type from the scratch.