I don't understand why T=c2e^-lamda(k)(t). Can you please explain it to me. Thank you b In Problems 1-16 use separation XA bartleby.com/solution-answer/chapter-121-problem-10e-differential-equations-with-boundary-value-problems-mindtap-course-list-9th-edition/9781337604918/in-problems-116-use-separation-of-variables-to-find-if-possible-product-solutions-for-th...= bartlebyQ Search for textbooks, step-by-step explanations to homework questions, ...E Ask an Experte Bundle: Differential Equations with Bou...< Chapter 12.1, Problem 10E >Problem 11EExplanation of SolutionThe given partial differential equation is k = , k > 0.Let the solution be u (x, t) = X (x) T (t).Now, differentiating u partially with respect to x and i gives*u = X"T and = XT'Substituting these values in the given partial differential equationbecomeskX"T = XT'k = 4* = = -1KTwhere l is the separation constant.On solving further it becomes,X" + AX = 0 and T' + AkT = 0On solving further it gives, T = c2e¬kt_For first differential equation consider three cases:When 1 = 0 the differential equation becomes X" = 0 which givesthe solution X = ax + b.Thus, the product solution is,u (x, t) = X (x) T (1)= (ax + b) (cze¬dkr)= e-0t (Ax + B)= Ax + BPrivacy · Terms

We have to explain the argument T=c2e^-lamda(k)(t) in the given solution.

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I don't understand why T=c2e^-lamda(k)(t). Can you please explain it to me. Thank you

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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I don't understand why T=c2e^-lamda(k)(t). Can you please explain it to me. Thank you

b In Problems 1-16 use separation X
A bartleby.com/solution-answer/chapter-121-problem-10e-differential-equations-with-boundary-value-problems-mindtap-course-list-9th-edition/9781337604918/in-problems-116-use-separation-of-variables-to-find-if-possible-product-solutions-for-th...
= bartleby
Q Search for textbooks, step-by-step explanations to homework questions, ...
E Ask an Expert
e Bundle: Differential Equations with Bou...
< Chapter 12.1, Problem 10E >
Problem 11E
Explanation of Solution
The given partial differential equation is k = , k > 0.
Let the solution be u (x, t) = X (x) T (t).
Now, differentiating u partially with respect to x and i gives
*u = X"T and = XT'
Substituting these values in the given partial differential equation
becomes
kX"T = XT'
k = 4
* = = -1
KT
where l is the separation constant.
On solving further it becomes,
X" + AX = 0 and T' + AkT = 0
On solving further it gives, T = c2e¬kt_
For first differential equation consider three cases:
When 1 = 0 the differential equation becomes X" = 0 which gives
the solution X = ax + b.
Thus, the product solution is,
u (x, t) = X (x) T (1)
= (ax + b) (cze¬dkr)
= e-0t (Ax + B)
= Ax + B
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