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Homework Statement
Find all solutions of the equation:
y' = (2y)/(t.logt) = 1/t, t > 0
Homework Equations
Integrating factor I = exp([tex]\int[/tex]p(x)dx)
where y' + p(x)y = q(x)
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