(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find all solutions of the equation:

y' = (2y)/(t.logt) = 1/t, t > 0

2. Relevant equations

Integrating factor I = exp([tex]\int[/tex]p(x)dx)

where y' + p(x)y = q(x)

3. The attempt at a solution

Hi everyone, here's what I've done so far:

Let p(t) = -2/(t.logt)

I = exp([tex]\int[/tex]((-2)/(t.logt))dt)

Factoring out the -2, consider [tex]\int[/tex]1/(t.logt)dt

Use integration by parts:

u = 1/logt

du = -(logt)^-2.(1/t).dt

dv = (1/t)dt

v = logt

[tex]\int[/tex]u.dv = uv - [tex]\int[/tex]v.du

I end up with:

[tex]\int[/tex]1/(t.logt)dt = 1 + [tex]\int[/tex]1/(t.logt)dt

which gives me 0 = 1, which is clearly wrong.

But I can't see where I'm going wrong! I've done it five times now and I keep getting the same answer. Can anyone see where I'm going wrong or suggest another way of solving the problem?

Thanks for any help

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# ODE question - Integrating factor

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