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

The formula for a particular solution given in (3.42) applies to the more general problem of solving y" + p(t)y' + q(t)y = f(t). In this case, y₁ and y₂ are independent solutions of the associated homogeneous equation y" + p(t)y' + q(t)y = 0. In the following, show that y₁ and y₂ satisfy the associated homogeneous equation, and then determine a particular solution of the inhomogeneous equation:

b.) ty" - (t + 1)y' + y = t²e^2t; y₁(t) = 1 + t, y₂(t) = e^t (answer should be: 1/2 (t -1) e^2t + 1/2 + t/2 )

c.) t²y" - 3ty' + 4y = t^5/2; y₁(t) = t², y₂(t) = t²ln(t) (answer should be: 4t^5/2 )

Expert Solution

Colby Messinger answered 1 year ago

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