Toronto Math Forum
MAT2442013F => MAT244 MathTests => MidTerm => Topic started 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*}

I will try to type this afterwards. See attachment

As promised:
$$ dy/dt + 2y/t = 1 \\
\mu (dy/dt) + 2y\mu/t = \mu \\
d/dt (\mu y) = d\mu/dt\cdot y + \mu\cdot dy/dt \\
\implies d\mu/dt\cdot y = 2y\mu/t \\
\implies \mu = t^2 \\
d/dt(t^2 y) = t^2 \\
\implies t^2 y = (1/3)t^3 + c \\
\implies y = (1/3)t + c/t^2
$$

2

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.

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 nonoversized version of my work...