MAT244-2013F > MidTerm

MT, P2

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Victor Ivrii:
Find the general solution of the ODE
y'+\frac{2}{t} y=1.

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:

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.


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