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Chapter 4, Section 4.7, QUestion 23 Given that the given functions yı and y2 satisfy the corresponding homogeneous equation;

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Answer #1

Given 1 3t 1 and 2e are solutions of the corresponding homogeneous equation. Therefore we can use the formula y1g(t) dt y2gtdt+ Y2 W(y1,y2) yp y1 W(yny2) where W (y1, y2)y1Y2- 4291 . Given g(t)81te .

Computing W gives us W (y1,y2) = 9tet

Thus the particular solution is:

et 81t e (3t1)81te dt Yp (3t 1) 3t -dt e 9tet 9te3t

Solving this integral, we get the answer 1 9te3t(9f 6t4)e

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