Solve an IVP ODE using the method of variation of parameters

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Solve an IVP ODE using the method of variation of parameters


Find the solution of the system X'
using the method of variation of parameters


2 0 0 cos(t)
X' = -1 0 -1 X + sin(t)
1 1 2 e^-t

that satisfies the intial condition

( 0 )
X(0) = 1
-1