Solve the given initial-value problem. x' = 1 2 0 1 − 1 2 x, x(0) = 2 7
1 answer:
I'll go out on a limb and guess the system is

with initial condition

. The coefficient matrix has eigenvalues

such that

The corresponding eigenvectors

are such that




So the characteristic solution to the ODE system is

When

, we have

from which it follows that

and

, making the particular solution to the IVP

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