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## Homework Statement

Find y2 given

t^2y'' + 3ty' + y = 0 y1(t) = 1/t

## Homework Equations

## The Attempt at a Solution

i found y, y' and y'' and plugged it back in to the Differential equation,

after doing some work, i'm basicly down to

tv''+v' = 0

where y2 = v/t

so u = v' and u' = v'' Plugging that in...

tu' + u = 0

how would i solve this for u?

i think its separable equations but that would give me

du/-u = dt/t

which would be ln (u) = -ln(t) + c .... u = 1/t +c so v' = 1/t +c which means v = lnt

pluging v into y2 would give me lnt/t

Sorry its kind of confusing but the answer's not in the back of the book and i need to know if i did this right

Thank you!