In and 3 2, verify that the function defined by the definite integral is a particular
Chapter 1, Problem 32(choose chapter or problem)
In and 3 2, verify that the function defined by the definite integral is a particular solution of the given differential equation. In both problems, use the Leibniz formula for the derivative of an integral: d iv(x) dv du iv(x) a dx F(x, t)dt = F(x, v(x)) dx -F(x, u(x)) dx + -F(x, t)dt.ry" + xy' + (x2 -n2)y = O; y(x) = - cos(x sin 8 -n8)d8, 7T 0 where n = 0, 1, 2, ... [Hint: After you have substituted y, y', and y" into the DE, then compute ! (x cos 8 + n) sin(x sin 8 - n8) and look around.]
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