This whole question is to do with a 1D heat equation.(adsbygoogle = window.adsbygoogle || []).push({});

This is where I get stuck

He has derived this far

Q'(t) = -Q(t) * (cb)^2

and

P''(x) = -P(x) * b^2

Now, his differntial equation for Q(t) is

Q(t) = Ae^-(cb)^2 t

and

P(x) = Bcos(bx) + Csin(bx)

How did he get these?

Only way I can think of is for the second one where i would rearrange into a homogeneous equation

P'' + b^2 P = 0

Where P = 0 or -b^2 (from auxillery eqn)

so the general solution would be P(x) = B + Ce^-b^2 x

But this isn't what he found..

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# Differential equation

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