Consider the initial value problem x' = X(0) 2t Form the complementary solution to the homogeneous equation. -e^t en-t x.(t) = ¤1 + a2 e^t e^-t help (formulas) help (matrices) Construct a particular solution by assuming the form x,(t) = ãe! + bt + č and solving for the undetermined constant vectors ā, b, and č. -1/3e^(2t)-1 help (formulas) š,(1) = help (matrices) 2/3e^(2t)-1 Form the general solution x(t) = x.(t) + x,(t) and impose the initial condition to obtain the solution of the initial value problem. x1(t) -e^t+e^-t-1/3e^(2t)-1 x2(t) e^t+e^-t+2/3e^(2t)-t help (formulas) help (matrices)

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