1) Consider the differential equation dr =r' = 2x + cos²t, r(0) = ro- dt i) Solve the differential equation (1) and explain the domain of the solution x(t).
1) Consider the differential equation dr =r' = 2x + cos²t, r(0) = ro- dt i) Solve the differential equation (1) and explain the domain of the solution x(t).
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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Transcribed Image Text:1) Consider the differential equation
dx
a' = 2x + cos? t, x(0) = ro-
dt
i) Solve the differential equation (1) and explain the domain of the solution x(t).
ii) Sketch the graph of the solution obtained in item i). Choose your initial condition 2(0) = 2o.
2) Consider the differential equation
dx
r' = -3x + cost + cos 2t, r(0) = ro.
dt
i) Solve the differential equation (2) and explain the domain of the solution x(t)
ii) Sketch the graph of the solution obtained in item i). Choose your initial condition (0) = ro.
3) Consider the differential equationa' = (cost + sin 2t)x, x(0) = xo.
i)Solve the above equation and sketch your solutions with the following initial conditions: (0)
x(0) = 1 e r(0) = -1.
ii) Sketch the graph of the function X(t) =¤(t)dt, with r(0) = 0 in each of the situations analyzed
n in item i). calculate lim-40 X (t).
= 0,
4)Consider the differential equation a' = (- tan t + sin 2t)æ, æ(0) = xo.
i) Solve the above equation and sketch your solutions with the initial conditions
x(2m) = 1. Plot the graph of x(t) in each of the 3 situations described.
Note: You can use computer resources. Note that has is not defined across the entire line.
r(0) = 0, x(7) = 1 and
5) Consider the differential equation of separate variables
dy
= / = Os 20, y(0) = y0
dæ
i) Solve equation (3) and calculate the domain of the solution y(x).
ii) Plot the graph of solution y.
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