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dY Given the initial value problem dt 2-1 d. whose matrix has a repeated %3D eigenvalue A = 1, find the general solution in terms of the initial conditions. x(t) form where Y(t) = ()- Write solution in component Your answers should have the variables p your and a in them. Enter an answer like (2p – g)te-3t as (2p-q)*te^(-3t). Please note the * in this expression!

dY Given the initial value problem dt 2-1 d. whose matrix has a repeated %3D eigenvalue A = 1, find the general solution in terms of the initial conditions. x(t) form where Y(t) = ()- Write solution in component Your answers should have the variables p your and a in them. Enter an answer like (2p – g)te-3t as (2p-q)*te^(-3t). Please note the * in this expression!

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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2 -1 Given the initial value problem dt CỸ,Ÿ(0) = (P) whose matrix has a repeated - 4 eigenvalue A = - 1, find the general solution in terms of the initial conditions. = (). x(t) Your answers should have the variables p y(t) )* Write your solution in component form where Y(t) and q in them. Enter an answer like (2p – q)te-3t as (2p-q)*te^(-3t). Please note the * in this expression! | Be sure to PREVIEW your answers before submitting! x(t) = y(t) = x(t) Preview: y(t) Preview:
Transcribed Image Text:2 -1 Given the initial value problem dt CỸ,Ÿ(0) = (P) whose matrix has a repeated - 4 eigenvalue A = - 1, find the general solution in terms of the initial conditions. = (). x(t) Your answers should have the variables p y(t) )* Write your solution in component form where Y(t) and q in them. Enter an answer like (2p – q)te-3t as (2p-q)*te^(-3t). Please note the * in this expression! | Be sure to PREVIEW your answers before submitting! x(t) = y(t) = x(t) Preview: y(t) Preview:
Expert Solution
Step 1

Given differential equation is,

dY→dt=2-19-4Y→ ,Y→0=pq

So, the characteristics equation of the given differential equation is,

λ+1λ+1=0λ2+2λ+1=0SI-A=λ2+2λ+1

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