Answered: Find a basis of solutions by the…

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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Need help on this linear algebra problem, thank you!!
V =R * R 10a6b T(") - (170-100) {(2)· (3)} B = { find the matrix representation of T with respect to beta. Then determine wether beta is a basis consisting of eigenvectors. I have got -2 [T]₁ = ( 2 4 this does not match answer key. What's wrong? please point it out and have the rest of solution to the problem. thanks!
2y" — 5y' + 2y = 0. ) Find two solutions. Show that the two solutions in part (a) form a fundamental set of solutions and find the general solution.
8) Use the method of Variation of Parameters to solve y" - y'= t. You - calculate determinants! can use MATHEMATICA to
solve 18 please
X' = {(1, 2), (4, 3)} x X + {(8e3t), (12e2t)}. Where X1 = {(-e-t), (e-t)} and X2 = {(e5t), (2e5t)} are solutions of the corresponding homogeneous system. Show that the solutions of the corresponding homogeneous system are linearly independent. Find the fundamental matrix and its inverse. Solve the nonhomogeneous system given above. Show all of your work and multiply out all matrix calculations.
Use Newton's method with the starting point (1,2)T to find a solution of the system +y 0 2+y = 1. The first iteration produces the vector (A) (2,2)T (B) (2,1) (C) (1,1)" (D) (1,2)" (E) none of the above O (A) O (B) O (C) O (D) O (E)
Q. No. 01 Solve the equation Ax = b by using LU decomposition 4 3 -51 2 А -4 -5 7 -4 8 6. -8] 6.
Use Frobenius method of Lecture 11, to find the first three non-zero terms of the solutions: 1?x" + x' + X = 0
Q1) Solve the following system of algebraic equations using matrix inverse method. 6 30-0 Q2/ Solve the following differential equations. 1) + y² - 4: 2) 7+3 / +2y=0 Q3/ Find points of intersection for the following curves. 1- r = 1+ cos 0, 2- r = 1 + sin 0.
(a) Verify that the given functions are linearly independent and form a basis of solutions of the given ODE. (b) Solve the IVP. Graph or sketch the solution.

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Find a basis of solutions by the frobenius method. Xy'' + 2y' + xy = 0