Consider the following problem (PDE) Let A E R.Consider the following problem2u" (x) + u' (x) = -Xu(x), 0 < x < 1,u'(0) = 0 , u(1) = 0.u +0(*)%3D1) Put v(x) = xu(x).Show that v satisfiesv"(x) = -Av(x) , 0

Name: Consider the following problem (PDE) Let A E R.Consider the following
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Description: Consider the following problem (PDE) Let A E R.Consider the following problem2u" (x) + u' (x) = -Xu(x), 0 < x < 1,u'(0) = 0 , u(1) = 0.u +0(*)%3D1) Put v(x) = xu(x).Show that v satisfiesv"(x) = -Av(x) , 0

Consider the problem (*)u''+2xu'=-λu, 0<x<1u'(0)=u(1)=0u≠0Let…

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Let A E R. Consider the following problem u" (x) + u (x) = -Xu(x), 0 < x < 1, u"(0) — 0 , и(1) — 0. u # 0 (*) 1) Put v(x) = xu(x).Show that v satisfies v" (x) = -Av(x), 0 < x < 1, о(0) — о(1) — 0, v 7 0. 2) Solve (**) and deduce the sequence of solutions of problem (**)

Let A E R. Consider the following problem u" (x) + u (x) = -Xu(x), 0 < x < 1, u"(0) — 0 , и(1) — 0. u # 0 (*) 1) Put v(x) = xu(x).Show that v satisfies v" (x) = -Av(x), 0 < x < 1, о(0) — о(1) — 0, v 7 0. 2) Solve () and deduce the sequence of solutions of problem ()

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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Topic Video

Question

Consider the following problem (PDE)

Let A E R.
Consider the following problem
2
u" (x) + u' (x) = -Xu(x), 0 < x < 1,
u'(0) = 0 , u(1) = 0.
u +0
(*)
%3D
1) Put v(x) = xu(x).Show that v satisfies
v"(x) = -Av(x) , 0 <x < 1,
v(0) = v(1) = 0,
v 7 0.
2) Solve (**) and deduce the sequence of solutions of problem (*).
(**)

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