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(Superposition Principle) Consider (п-1) Any(n) + an-1Y +... + a1y' + aoy = f1(t) + f2(t) +... + fm(t) where an, ...a1, ao E R, and an # 0. Suppose also that y:(t) is a solution to any(n) + an-1y(n-1) + ... + a1y' + aoy = derivative to justify why k1y1(t) + k2Y2(t) + ... + kimYm (t) is a solution to ,(n) fi(t), where 1 < i< m. Use the linearity of the Any (п-1) + an-1y +... + a1y' + aoy = = f1(t)+ f2(t)+... + fm(t), where k1, k2, ., kim E R.

(Superposition Principle) Consider (п-1) Any(n) + an-1Y +... + a1y' + aoy = f1(t) + f2(t) +... + fm(t) where an, ...a1, ao E R, and an # 0. Suppose also that y:(t) is a solution to any(n) + an-1y(n-1) + ... + a1y' + aoy = derivative to justify why k1y1(t) + k2Y2(t) + ... + kimYm (t) is a solution to ,(n) fi(t), where 1 < i< m. Use the linearity of the Any (п-1) + an-1y +... + a1y' + aoy = = f1(t)+ f2(t)+... + fm(t), where k1, k2, ., kim E R.

Advanced Engineering Mathematics
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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(Superposition Principle) Consider Any(n) (п-1) + an-1y +... + a1y' +aoy = f1(t) + f2(t) + ... + fm(t) where an, ...a1, ao E R, and an # 0. Suppose also that y:(t) is a solution to any(n) + an-1y(n-1) + ... + a1y' + aoy = derivative to justify why k1y1(t) + k2y2(t) + ... + kmYm (t) is a solution to ,(n) fi(t), where 1 < i< m. Use the linearity of the Any (п-1) + an-1y' +... + a1y' + aoy = = f1(t) + f2(t)+... + fm(t), where k1, k2, .., kim E R.
Transcribed Image Text:(Superposition Principle) Consider Any(n) (п-1) + an-1y +... + a1y' +aoy = f1(t) + f2(t) + ... + fm(t) where an, ...a1, ao E R, and an # 0. Suppose also that y:(t) is a solution to any(n) + an-1y(n-1) + ... + a1y' + aoy = derivative to justify why k1y1(t) + k2y2(t) + ... + kmYm (t) is a solution to ,(n) fi(t), where 1 < i< m. Use the linearity of the Any (п-1) + an-1y' +... + a1y' + aoy = = f1(t) + f2(t)+... + fm(t), where k1, k2, .., kim E R.
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