At 16:08, please correct me if I'm wrong, but did you substitute the constants back into the particular solution correctly? a1 = -1/3, a2 = 1/3, b1 = -3, and b2 = -2/3. Wouldn't this make the particular solution [1/3 -2/3]cost + [-1/3 -3]sint? By the way, I love your videos! They have been so incredibly beneficial, especially given that my class is using the same textbook and the professor isn't being very helpful in breaking the material down to a digestible degree. Thank you for posting these to the public!
Hey this is a super late response but hopefully this can help some people in the future- the correct solution to the matrix is a1= -1/3 a2=-3 b1=1/3 b2=-2/3 I believe he wrote the solutions in the wrong order when he wrote the RREF of the matrix, swapping the values for a2 and b1. Then he mistakenly used the values for a1 and b1 for sint and the values for a2 and b2 for cost. Therefore the particular solution should be Xp = [-1/3, 1/3] cost + [-3, -2/3] sint.
At 16:08, please correct me if I'm wrong, but did you substitute the constants back into the particular solution correctly? a1 = -1/3, a2 = 1/3, b1 = -3, and b2 = -2/3. Wouldn't this make the particular solution [1/3 -2/3]cost + [-1/3 -3]sint? By the way, I love your videos! They have been so incredibly beneficial, especially given that my class is using the same textbook and the professor isn't being very helpful in breaking the material down to a digestible degree. Thank you for posting these to the public!
Hey this is a super late response but hopefully this can help some people in the future- the correct solution to the matrix is
a1= -1/3
a2=-3
b1=1/3
b2=-2/3
I believe he wrote the solutions in the wrong order when he wrote the RREF of the matrix, swapping the values for a2 and b1.
Then he mistakenly used the values for a1 and b1 for sint and the values for a2 and b2 for cost.
Therefore the particular solution should be Xp = [-1/3, 1/3] cost + [-3, -2/3] sint.