Consider the linear homogeneous system x_ = p11(t) x + p12(t) y, y_ = p21(t) x + p22(t)
Chapter 7, Problem 12(choose chapter or problem)
Consider the linear homogeneous system x_ = p11(t) x + p12(t) y, y_ = p21(t) x + p22(t) y. Show that if x = x1(t), y = y1(t) and x = x2(t), y = y2(t) are two solutions of the given system, then x = c1x1(t) + c2x2(t), y = c1 y1(t) + c2 y2(t) is also a solution for any constants c1 and c2. This is the principle of superposition; it will be discussed in much greater detail in Section 7.4. 1
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