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Find the solution of the following problems. Before doing these problems, you might want to review...

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Advance Math

Find the solution of the following problems. Before doing theseproblems, you might want to review Exercise 3** on page 63:

d.) xy" + y' = x, where y(1) = 1m and y'(1) = -1 (answer shouldbe y(x) = 1/4 x2 - 3/2 ln(x) + 3/4)

e.) (x-1)2y" + (x-1)y' - y = 0, where y(2) = 1, andy'(2) = 0 (answer should be: y(x) = 1/2 (x-1)-1 + x/2 -1/2)

**Exercise 3: 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 areindependent solutions of the associated homogeneous equation y" +p(t)y' + q(t)y = 0.

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