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(d) Find the solution of the inhomogeneous initial value problem i = Az +9 z(0) = 20, in the case that -3 1 A = 0 and g:R+ C, 9(t) = -3 1 z0 = -2 -3 where a e R.

(d) Find the solution of the inhomogeneous initial value problem i = Az +9 z(0) = 20, in the case that -3 1 A = 0 and g:R+ C, 9(t) = -3 1 z0 = -2 -3 where a e R.

Advanced Engineering Mathematics
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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part D

(a) State the definition of linear independence of the functions f1, f2,..., fk : R → C" for k eN. 2. (b) Given A e Cnxn, for n e N, state the formula for the general solution ot the homogeneous ordinary differential equation (ODE) (2) i = Ax, defining all terms you introduce. (c) Find the general solution of (2) in the case that -3 1 A = -3 -3 (d) Find the solution of the inhomogeneous initial value problem * - Aa +9 x(0) = x0, in the case that -3 A = -3 and g:R+ C, g(t) = 1. -3 where a ER. (e) Comment on any qualitative dependence of the solution r in part (d) on the parameter a €R.
Transcribed Image Text:(a) State the definition of linear independence of the functions f1, f2,..., fk : R → C" for k eN. 2. (b) Given A e Cnxn, for n e N, state the formula for the general solution ot the homogeneous ordinary differential equation (ODE) (2) i = Ax, defining all terms you introduce. (c) Find the general solution of (2) in the case that -3 1 A = -3 -3 (d) Find the solution of the inhomogeneous initial value problem * - Aa +9 x(0) = x0, in the case that -3 A = -3 and g:R+ C, g(t) = 1. -3 where a ER. (e) Comment on any qualitative dependence of the solution r in part (d) on the parameter a €R.
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