12. Consider the linear homogeneous systemx' = P1(t)x + P12(1) y,y' = P21(1)x + P22(1) y.%3Dx2(t), y = y2(t)Show that if x = x1(t), y = yi(t) and x = x2(t), y = y½(t)are two solutions of the given system, then x = c1x¡(t) + c2X2(t),y = ciy1(t) + c2y2(t) is also a solution for any constants c¡ andC2. This is the principle of superposition; it will be discussed in muchgreater detail in Section 7.4.

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Answered: 12. Consider the linear homogeneous…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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