Duhamel principle to solve system of nonhomogeneous differential equations

Introduction : In this question, We will apply Duhamel principle to solve system of nonhomogeneous differential equations u’=v+2e^(-4t),v’=u-e^t , u(0)=-1/2,v(0)=2.Question : Apply Duhamel principle to solve system of non homogeneous differential equations\[\left(\begin{array}{c}u'(t) \\v'(t) \end{array}\right)=\left(\begin{array}{cc}0 & 1 \\1 & 0 \end{array}\right)\left(\begin{array}{c}u(t)…

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