Please note that the matrices are 2 by 2 and 2 by 1. Consider the initial value problem x'(t) = Ax(t), for t >= 0, with A = [[6, 5], [7, 8]] and x(0) = [[-13], [-11]]. Solve the initial value problem x(t) =
Added by Carolina F.
Step 1
Step 1: The general solution to the system x'(t) = Ax(t) is given by x(t) = e^(At)x(0), where e^(At) is the matrix exponential of At. Show more…
Show all steps
Close
Your feedback will help us improve your experience
Sri K and 67 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Recall that X = Φ(t)Φ⁻¹(t₀)X₀ + Φ(t) ∫[t₀ to t] Φ⁻¹(s)F(s) ds solves the initial value problem X' = AX + F(t), X(t₀) = X₀ whenever Φ(t) is a fundamental matrix of the associated homogeneous system. Use the above to solve the given initial-value problem. X' = (3 1; 1 3)X + (8e^4t; 8e^2t), X(0) = (1; 1) X(t) = e^2t<-1,1> + e^4t<1,1> + te^2t<-1,1> + te^4t<1,1>
Sri K.
Given the matrix A = [2 1; 1 2], Y1 = [e^3t; e^3t], Y2 = [e^t; -e^t], k = [2; 8] What are the values of c1 and c2 in the solution to the initial value problem y' = Ay and y(0) = k y = c1 [e^3t; e^3t] + c2 [e^t; -e^t]
Madhur L.
Using the differential operator method, find a fundamental matrix for the system and write the general solution as a matrix: If initial values are given, solve the initial value problem: x1' = x1 - 2x2, x2' = -6x1; x1(0) = 1, x2(0) = -19
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD