(r) (Of1/əx1) (afi/ax) (af2/dx1) (a2/ax)") Ar? -0.5743 2.0000 30.2494 -0.5436 13.4461 3.8772 0.7720 -0.0059 -0.0057 5.51 x 10-6 0.0 2.0000 15.4731 8.3891 25.5060 7.3133 5.1395 3.8541 3.9830 3.7127 15.7781 9.6024 7.3591 6.1183 6.4358 6.4366 6.4366 1.4247 1.0713 6.4354 -0.3544 --0.0138 -0.0591 0.00159 1.4564 -0.3106 12.5880 6.8067 5.5679 5.4244 3.4806 -0.1878 0.0417 0.000368 1.1457 1.3802 0.1290 2.7149 2.7126 2.7183 2.7183 4 1.0575 0.9984 1.0000 0.9579 --0.0122 0.9996 1.0000 3.7183 3.7183 5.4366 5.4366 12.1 x 106 6. 2.86 x 10 6 -3.0 x 10 1.0000 -2 x 109 1.0000

(r) (Of1/əx1) (afi/ax) (af2/dx1) (a2/ax)") Ar? -0.5743 2.0000 30.2494 -0.5436 13.4461 3.8772 0.7720 -0.0059 -0.0057 5.51 x 10-6 0.0 2.0000 15.4731 8.3891 25.5060 7.3133 5.1395 3.8541 3.9830 3.7127 15.7781 9.6024 7.3591 6.1183 6.4358 6.4366 6.4366 1.4247 1.0713 6.4354 -0.3544 --0.0138 -0.0591 0.00159 1.4564 -0.3106 12.5880 6.8067 5.5679 5.4244 3.4806 -0.1878 0.0417 0.000368 1.1457 1.3802 0.1290 2.7149 2.7126 2.7183 2.7183 4 1.0575 0.9984 1.0000 0.9579 --0.0122 0.9996 1.0000 3.7183 3.7183 5.4366 5.4366 12.1 x 106 6. 2.86 x 10 6 -3.0 x 10 1.0000 -2 x 109 1.0000

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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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Solve the simultaneous, nonlinear equations
x₁ ln x₂ + x₂ exp( x₁) =ex(1)
x₂ ln x₁+ 2x₁ exp (x₂) =2 exp(1)
for x₁ and x₂ to within ± 0.001, by the Newton–Raphson method.

(r)
(Of1/əx1) (afi/ax) (af2/dx1)
(a2/ax)")
Ar?
-0.5743
2.0000
30.2494
-0.5436
13.4461
3.8772
0.7720
-0.0059
-0.0057
5.51 x 10-6
0.0
2.0000
15.4731
8.3891
25.5060
7.3133
5.1395
3.8541
3.9830
3.7127
15.7781
9.6024
7.3591
6.1183
6.4358
6.4366
6.4366
1.4247
1.0713
6.4354
-0.3544
--0.0138
-0.0591
0.00159
1.4564
-0.3106
12.5880
6.8067
5.5679
5.4244
3.4806
-0.1878
0.0417
0.000368
1.1457
1.3802
0.1290
2.7149
2.7126
2.7183
2.7183
4
1.0575
0.9984
1.0000
0.9579
--0.0122
0.9996
1.0000
3.7183
3.7183
5.4366
5.4366
12.1 x 106
6.
2.86 x 10 6
-3.0 x 10
1.0000
-2 x 109
1.0000

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