solve the IVP 4ft = 4 Uxx Utt 11(x 10) = ²x²₁ e ( ( -00o 14₂ (x10) = x èx² xe Any Integrals must be evaluated. -84x20. Any Using D'Alembert's solution x+ct u(x₁t) = { [ f(x+et) + f(x-et) ] + £c √x-et g(s) ds with and c = 2. f(x) = 2x²₁ g(x) = x ( 1 then 3. UG₁e) = { [ē (x+²6)² = (x-26) ²] - [ē (2+2+)² ē (x-2)²3
solve the IVP 4ft = 4 Uxx Utt 11(x 10) = ²x²₁ e ( ( -00o 14₂ (x10) = x èx² xe Any Integrals must be evaluated. -84x20. Any Using D'Alembert's solution x+ct u(x₁t) = { [ f(x+et) + f(x-et) ] + £c √x-et g(s) ds with and c = 2. f(x) = 2x²₁ g(x) = x ( 1 then 3. UG₁e) = { [ē (x+²6)² = (x-26) ²] - [ē (2+2+)² ē (x-2)²3
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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Question
023
Please show all the steps
![Problem 23.
solve the IVP
Utt
(
1(x ₁0) = x²₁
11₂ (x₁0) = x = x²
Any Integrals must be evaluated.
=
then
4 Uxx
-00<x<001
(
ост
87x780-
Any Using D'Alembert's solution
x+ck
20
u(x₁t) = = [ f(x+et) + f(x-et) ] + £c √xet g(s) ds
f(x) = ēx²₁ g(x)= x @ ²²
and c = 2.
with
(
3.
-(x-21) 2
2
(78-x) -² -2 (78 + x)² -14 - [8 (78-x) ² + +(786+2) ²³ 37 = (2²49)
x)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9c55fd55-ae67-4b97-a36c-91359ff73a6f%2F3d05f2d9-7414-4eeb-94ef-97a0825c7220%2Fp4xwpm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 23.
solve the IVP
Utt
(
1(x ₁0) = x²₁
11₂ (x₁0) = x = x²
Any Integrals must be evaluated.
=
then
4 Uxx
-00<x<001
(
ост
87x780-
Any Using D'Alembert's solution
x+ck
20
u(x₁t) = = [ f(x+et) + f(x-et) ] + £c √xet g(s) ds
f(x) = ēx²₁ g(x)= x @ ²²
and c = 2.
with
(
3.
-(x-21) 2
2
(78-x) -² -2 (78 + x)² -14 - [8 (78-x) ² + +(786+2) ²³ 37 = (2²49)
x)
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