can someone please help explain how to solve 24d will rate asap! this is problem 23:
Posted: Thu May 12, 2022 8:36 am
can someone please help explain how to solve 24d
will rate asap!
this is problem 23:
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
will rate asap!
- Can Someone Please Help Explain How To Solve 24d Will Rate Asap This Is Problem 23 1 (42.46 KiB) Viewed 27 times
- Can Someone Please Help Explain How To Solve 24d Will Rate Asap This Is Problem 23 2 (69.93 KiB) Viewed 27 times
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