Undefined Terms Within Series Solution For Heat Equation

alahovom7ahc

alahovom7ahc

Answered question

2022-04-10

Undefined Terms Within Series Solution For Heat Equation Solution
ut=4u×,t>0, 0<x<π,
ux(0,t)=ux(π, t)=0, t>0
u(x,0)=2cos(2x)+5cos(3x),0xπ

Answer & Explanation

o2z1zsjj0

o2z1zsjj0

Beginner2022-04-11Added 10 answers

Step 1
Using the Laplace transform
sU(x,s)=4U×(x,s)+2cos(2x)+5cos(3x),
Ux(0,s)=Ux(π,s)=0
Solving for x we have
U(x,s)=2scos(2x)s+16+5cos(3x)s+36
and after inversion
u(x,t)=2e16tcos(2x)+5e36tcos(3x)

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