can someone please help explain how to solve 24d
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Can Someone Please Help Explain How To Solve 24d Will Rate Asap This Is Problem 23 1 (42.46 KiB) Viewed 28 times
this is problem 23:
Can Someone Please Help Explain How To Solve 24d Will Rate Asap This Is Problem 23 2 (69.93 KiB) Viewed 28 times
24. Solve the following Cauchy-Euler equations by using the substitution described in Problem 23 to change them to constant coefficient equations, finding their general solutions by the methods of the preceding sections, and restoring the original independent variable t. (a) 12Y" + ty' – 9y = 0 (b) t’y" + 3ty' + 10y = 0 (c) t’y" + 3ty' + y = [+++! (d) 1?" + ty' +9y = -tan ( 3 Int)
23. To justify the solution formulas (8) and (9), perform the following analysis. (a) Show that if the substitution t = el is made in the function y(t) and x is regarded as the new inde- pendent variable in Y(x) = y(e"), the chain rule implies the following relationships: dy dY d?y dY dt dx dx (b) Using part (a), show that if the substitution t = et is made in the Cauchy-Euler differential equation (6), the result is a constant-coefficient equation for Y(x) = y(ek), namely, d²Y dY (20) + (b-a) +cY = f(e"). = dx t Rd df2 dx2 a dr2
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