Question
Consider the second order constant coefficient linear differential equation with initial values y '' ? 3y ' + 2y = e 3t , y(0) =
Consider the second order constant coefficient linear differential equation with initial values y'' ? 3y' + 2y = e3t , y(0) = 0, y' (0) = 3 .
(a) Find the characteristic polynomial q(s), then find the set Bq.
(b) The Bq in Part (1) should contain two functions. Denote these two functions by y1 and y2. Use variation of parameters to find a particular solution yp toy'' ? 3y' + 2y = e3t .
(c) Now the solution to the initial value problem is of the form yp + c1y1 + c2y2 for some undetermined constants c1, c2 ? R. Use the initial values to determine c1 and c2.
(d) From another point of view, y satisfies a system of first order linear differential equations. (question continues in picture)
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started