3. (i) Show that applying the Euler Lagrange equation to the functional (w*++295(1) de leads to the second order differe

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3 I Show That Applying The Euler Lagrange Equation To The Functional W 295 1 De Leads To The Second Order Differe 1 (27.92 KiB) Viewed 21 times

3. (i) Show that applying the Euler Lagrange equation to the functional (w*++295(1) de leads to the second order differential equation y" - y = f(1). (ii) The rest of this problem recalls the variation of parameters method of solving this equation. Show that if we set y = ue* + ve* for two new variables u and v, and assume the convenient relationship u'et +ve+ = 0 (CRI) 1 between u and v, we get the pair of first order equations = f(x) and t'= x s(r). Why is (CRI) a convenient relationship? (iii) Choose a nonconstant function f(t) and find u, v, and y. -