Query 24 Differential Equations

Question:  Verify Abel's Theorem in the interval (-infinity, infinity) for

y ' = [ 6, 5; -7, -6] * y

whose solutions are

y_1 = [ 5 e^-t; -7 e^-t ]

y_2 = [ e^t; - e^t ]

with t_0  = -1

Your solution: 

Confidence rating:
 

Given Solution: 

Self-critique (if necessary):

Self-critique rating:

Question:  y ' = A y, with solutions

y_1 = [5; 1]

y_2 = [2 e^(3 t), e^(3 t) ]

Verify that this constitutes a fundamental set.

Find Tr(A).

Show that

psi(t) = [y_1, y_2]

satisfies

psi ' = A * psi

Find A by finding psi ' * psi^-1

Is the result consistent with your result for the trace of A?

Your solution: 

Confidence rating:
 

Given Solution: 

Self-critique (if necessary):

Self-critique rating:

Question: 

Your solution: 

Confidence rating:
 

Given Solution: 

Self-critique (if necessary):

Self-critique rating: