1. Use separation of variables to find a product solution to the following: A. B. C. D. 2²u əx² k- ди at' k>0 u = e-t (A₁eka²t cosh ax + B₁eka²t sinh ax) u = e-t (A₂e-ka²t cos ax + B₂e-ka²t sin ax) u = et(A3x + B3) u = e-t (A₁e-ka²t cosh ax + B₁e cosh ax + B₁e-ka²t sinh ax) e-t (A₂eka²t cos ax + B₂eka²t sin ax) u = e-t (A3x + B3) u = et (A₁eka²t cosh ax + B₁eka²t sinh ax) 1 = e¹(A₂e-ka²t cos ax + B₂e-ka²t sin ax) u = et (A3x + B3) u = et (A₁e-ka²¹t cosh ax + B₁e-ka²t sinh ax) u = et (A₂eka²t cos ax + B₂eka²t sin ax) u = et (A3x + B3)
1. Use separation of variables to find a product solution to the following: A. B. C. D. 2²u əx² k- ди at' k>0 u = e-t (A₁eka²t cosh ax + B₁eka²t sinh ax) u = e-t (A₂e-ka²t cos ax + B₂e-ka²t sin ax) u = et(A3x + B3) u = e-t (A₁e-ka²t cosh ax + B₁e cosh ax + B₁e-ka²t sinh ax) e-t (A₂eka²t cos ax + B₂eka²t sin ax) u = e-t (A3x + B3) u = et (A₁eka²t cosh ax + B₁eka²t sinh ax) 1 = e¹(A₂e-ka²t cos ax + B₂e-ka²t sin ax) u = et (A3x + B3) u = et (A₁e-ka²¹t cosh ax + B₁e-ka²t sinh ax) u = et (A₂eka²t cos ax + B₂eka²t sin ax) u = et (A3x + B3)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
answer 1 only
Transcribed Image Text:1. Use separation of variables to find a product solution to the following:
a²u
k -U=
dx2
A.
B.
C.
D.
B.
C.
Hint: No need to separate into 3 cases
A.
D.
u = e-t (A₁eka²t cosh ax + B₁eka²t sinh ax)
u = e-t (A₂e-ka²t cos ax + B₂e-ka²t sin ax)
u = e-t (A3x + B3)
-ka²t
u=e¹ (A₁e-ka²t
cosh ax + B₁e sinhax)
u = et (A₂eka²t cos ax + B₂eka²t sin ax)
u = et (A3x + B3)
2. Use separation of variables to find a product solution to the following:
ди
at
u = e-t
e-t(A₁e-ka²t cosh ax + B₁e-ka²t sinh ax)
u = e-t (A₂eka²t cos ax + B₂eka²t sin ax)
u = e-t (A3x + B3)
u = et (A₁eka²t cosh ax + B₁eka²t sinh ax)
u = et (A₂e-ka²t cos ax + B₂e-ka²t sin ax)
u = et (A3x + B3)
X
du
əx
= y
u = C₁
k> 0
du
dy
u = C₁
C₂
G₂₁ (1) ²²
u = C₁x²²yC₂-1
u = c₁(xy) c2
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