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

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

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

e.) (x-1)²y" + (x-1)y' - y = 0, where y(2) = 1, and y'(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 are independent solutions of the associated homogeneous equation y" + p(t)y' + q(t)y = 0.

Please show work!

Expert Solution

Colby Messinger answered 1 year ago

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