Let us solve the following equation via separation of variables J²u(x, t) Ət² = 7 d²u(x, t) ?х2 a) After using the ansatz u(x, t) = X(x)T(t), which equations do you get? Pick only two. (below C' denotes a constant) 8²T(t) 0² X(x) 0²T(t) 0 8²X(x) əx² X(x) √7CT(t) 8²T(t) 01² = = CX(x) 1 T(t) 0 Ət² əx² 81² 0² X(x) √C X(x) əx² = = = = 7CT(t)
Let us solve the following equation via separation of variables J²u(x, t) Ət² = 7 d²u(x, t) ?х2 a) After using the ansatz u(x, t) = X(x)T(t), which equations do you get? Pick only two. (below C' denotes a constant) 8²T(t) 0² X(x) 0²T(t) 0 8²X(x) əx² X(x) √7CT(t) 8²T(t) 01² = = CX(x) 1 T(t) 0 Ət² əx² 81² 0² X(x) √C X(x) əx² = = = = 7CT(t)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Let us solve the following equation via separation of variables
J²u(x, t)
Ət²
= 7
d²u(x, t)
?х2
a)
After using the ansatz u(x, t) = X(x)T(t), which equations do you get? Pick only two. (below C' denotes a constant)
8²T(t)
0² X(x)
0²T(t)
0
8²X(x)
əx²
X(x)
√7CT(t)
8²T(t)
01²
=
= CX(x)
1 T(t)
0
Ət²
əx²
81²
0² X(x)
√C X(x)
əx²
=
=
=
= 7CT(t)
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