# Toronto Math Forum

## MAT244-2013F => MAT244 Math--Tests => MidTerm => Topic started by: Victor Ivrii on October 09, 2013, 07:20:55 PM

Title: MT, P2
Post by: Victor Ivrii on October 09, 2013, 07:20:55 PM
Find the general solution of the ODE
\begin{equation*}
y'+\frac{2}{t} y=1.
\end{equation*}
Title: Re: MT, P2
Post by: Xuewen Yang on October 09, 2013, 09:51:41 PM
I will try to type this afterwards. See attachment
Title: Re: MT, P2
Post by: Xuewen Yang on October 09, 2013, 10:27:34 PM
As promised:

$$dy/dt + 2y/t = 1 \\ \mu (dy/dt) + 2y\mu/t = \mu \\ d/dt (\mu y) = d\mu/dt\cdot y + \mu\cdot dy/dt \\ \implies d\mu/dt\cdot y = 2y\mu/t \\ \implies \mu = t^2 \\ d/dt(t^2 y) = t^2 \\ \implies t^2 y = (1/3)t^3 + c \\ \implies y = (1/3)t + c/t^2$$
Title: Re: MT, P2
Post by: Xiaozeng Yu on October 09, 2013, 10:39:24 PM
2
Title: Re: MT, P2
Post by: Victor Ivrii on October 10, 2013, 06:39:57 AM
Xuewen Yang,

good job, for multiplication do not use * (it is a convolution, different operation) use either \cdot like in $a\cdot b$ or \times like $a\times b$.

Xiaozeng Yu, no point to post inferior solution (scan) after superior (typed) has been posted. This time I awarded "scan posted after scan", but not in the future.
Title: Re: MT, P2
Post by: Xiaozeng Yu on October 10, 2013, 09:27:59 AM
Xuewen Yang,

good job, for multiplication do not use * (it is a convolution, different operation) use either \cdot like in $a\cdot b$ or \times like $a\times b$.

Xiaozeng Yu, no point to post inferior solution (scan) after superior (typed) has been posted. This time I awarded "scan posted after scan", but not in the future.

sorry, it took me a while figuring out how to post the non-oversized version of my work...