Question: (i) Show that if u(x) solves the Euler equation then v(t) = u(et) solves a linear, constant coefficient differential equation. (ii) Use this alternative technique

(i) Show that if u(x) solves the Euler equation

then v(t) = u(et) solves a linear, constant coefficient differential equation.
(ii) Use this alternative technique to solve the Euler differential equations in Exercise 7.4.11.
Exercise 7.4.11
(a) x2u" + 5xu' - 5u = 0
(b) 2x2u" - xu' - 2u = 0
(c) x2u" - u = 0
(d) x2u" + xu' - 3u = 0
(e) 3x2u" - 5xu' - 3u = 0
(f)

dau du du 2 du

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