Author Topic: MT, P2  (Read 1917 times)

Victor Ivrii

  • Administrator
  • Elder Member
  • *****
  • Posts: 1332
  • Karma: 0
    • View Profile
    • Personal website of Victor Ivrii
MT, P2
« 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*}

Xuewen Yang

  • Full Member
  • ***
  • Posts: 17
  • Karma: 8
    • View Profile
Re: MT, P2
« Reply #1 on: October 09, 2013, 09:51:41 PM »
I will try to type this afterwards. See attachment

Xuewen Yang

  • Full Member
  • ***
  • Posts: 17
  • Karma: 8
    • View Profile
Re: MT, P2
« Reply #2 on: October 09, 2013, 10:27:34 PM »
As promised:

$$ dy/dt + 2y/t = 1 \\
     \mu (dy/dt) + 2y\mu/t = \mu \\
     d/dt (\mu y) = d\mu/dt\cdot y + \mu\cdot dy/dt \\
    \implies d\mu/dt\cdot y = 2y\mu/t \\
    \implies \mu = t^2 \\
     d/dt(t^2 y) = t^2 \\
    \implies t^2 y = (1/3)t^3 + c \\
    \implies y = (1/3)t + c/t^2
$$
« Last Edit: October 10, 2013, 06:34:23 AM by Victor Ivrii »

Xiaozeng Yu

  • Full Member
  • ***
  • Posts: 16
  • Karma: 4
    • View Profile
Re: MT, P2
« Reply #3 on: October 09, 2013, 10:39:24 PM »
2

Victor Ivrii

  • Administrator
  • Elder Member
  • *****
  • Posts: 1332
  • Karma: 0
    • View Profile
    • Personal website of Victor Ivrii
Re: MT, P2
« Reply #4 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.

Xiaozeng Yu

  • Full Member
  • ***
  • Posts: 16
  • Karma: 4
    • View Profile
Re: MT, P2
« Reply #5 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...