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The formula for a particular solution given in (3.42) applies to the more general problem of...

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Advance Math

The formula for a particular solution given in (3.42) applies tothe more general problem of solving y\" + p(t)y' + q(t)y = f(t). Inthis case, y1 and y2 are independentsolutions of the associated homogeneous equation y\" + p(t)y' +q(t)y = 0. In the following, show that y1 andy2 satisfy the associated homogeneous equation, and thendetermine a particular solution of the inhomogeneous equation:

b.) ty\" - (t + 1)y' + y = t2e2t;y1(t) = 1 + t, y2(t) = et (answershould be: 1/2 (t -1) e2t + 1/2 + t/2 )

c.) t2y\" - 3ty' + 4y = t5/2;y1(t) = t2, y2(t) =t2ln(t) (answer should be: 4t5/2 )

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