3. Consider the simultaneous equations h(r.y.)-(y--1) 0, fa(z, y.) (zy+-15y) 0, fs(r.y.) (2y² +-6) -0. (a). Obtain the Jacobian matrix for the system of equations. (b). For initial guesses z 2, y 2, and z 2, obtain one solution, a set of z, y, and a, using Matlab function fsolve. (c). Obtain a master equation in y by expressing in terms of y, z in terms of y, and finally two relations for a in terms of y. Identify all roots of the master equation using the Matlab function roots(coeff). Obtain the corresponding z and z. (d). Try to obtain all real roots of the system of equations using Matlab function fsolve.
3. Consider the simultaneous equations h(r.y.)-(y--1) 0, fa(z, y.) (zy+-15y) 0, fs(r.y.) (2y² +-6) -0. (a). Obtain the Jacobian matrix for the system of equations. (b). For initial guesses z 2, y 2, and z 2, obtain one solution, a set of z, y, and a, using Matlab function fsolve. (c). Obtain a master equation in y by expressing in terms of y, z in terms of y, and finally two relations for a in terms of y. Identify all roots of the master equation using the Matlab function roots(coeff). Obtain the corresponding z and z. (d). Try to obtain all real roots of the system of equations using Matlab function fsolve.
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
P1
Transcribed Image Text:3. Consider the simultancous equations
f(r.y.) (y--1) 0,
Sa(z, y. ) (zy+ - 15y) =0,
fs(z, y. ) = (2y² + -6) = 0.
(a). Obtain the Jacobian matrix for the system of equations.
(b). For initial guesses z 2, y- 2, and z 2, obtain one solution, a set of r, y, and 2, using
Matlab function fsolve.
(c). Obtain a master equation in y by expressing in terms of y, z in terms of y, and finally two
relations for a in terms of y. Identify all roots of the master equation using the Matlab function
roots(coelf). Obtain the corresponding z and s.
(d). Try to obtain all real roots of the system of equations using Matlab function fsolve.
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