MT, P2

[Victor Ivrii]

Find the general solution of the ODE
\begin{equation*}
y'+\frac{2}{t} y=1.
\end{equation*}

[Xuewen Yang]

I will try to type this afterwards. See attachment

[Xuewen Yang]

As promised:

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

[Xiaozeng Yu]

2

[Victor Ivrii]

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]

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...