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mudweez0009
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Homework Statement
Solve d2θ/dη2 + 2η(dθ/dη) = 0, to obtain θ as a function of η,
where θ=(T-T0)/(Ts-T0)
EDIT: I should add that this is a multi-part problem, and η is given as η=Cxtm. We had to use that to derive the equation in question above.. So I don't know if this is supposed to be solved as a non-constant coefficient method or not... My method below solved it assuming η was a constant.. I can supply the whole problem as an attachment if necessary.
Homework Equations
ay"+by'+cy=0
ar2+br+c=0
If the roots are real and different, solution is: y=aer1x+ber2x
The Attempt at a Solution
I would assume this can just be:
θ"+2ηθ'=0
which turns to:
r2+2ηr=0
But when using the quadratic equation to get roots, I get r1=-2η, and r2=0
Plug this into the solution form and get θ=ae-2ηx
Not sure if this is right. Can someone confirm, or tell me what I'm doing wrong? Thanks!
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