datorle43.html

restart; -1; with(LinearAlgebra); -1

`:=`(P, Matrix(%id = 5151664))

`:=`(lambda, T, Eigenvectors(P))

`:=`(v, Transpose(T))

`:=`(x, Transpose(`+`(`*`(c[1], `*`(exp(`*`(t, `*`(lambda[1]))), `*`(v[1]))), `*`(c[2], `*`(exp(`*`(t, `*`(lambda[2]))), `*`(v[2]))))))

`+`(map(diff, x, t), `-`(Typesetting:-delayDotProduct(P, x)))

`:=`(eq, {eval(x[1], t = 0) = 4, eval(x[2], t = 0) = 0})

{`+`(c[1], c[2]) = 0, `+`(`*`(I, `*`(c[1])), `-`(`*`(`+`(I), `*`(c[2])))) = 4}

`:=`(const, solve(eq))

{c[1] = `+`(`-`(`*`(2, `*`(I)))), c[2] = `*`(2, `*`(I))}

`:=`(y, map(eval, x, const))

plot(y, t = -5 .. 1, thickness = 2)

Plot_2d