26-2. Find the same minimum of 26-1 using Lagrange's undetermined multiplier method. Define the Langrangian by L=(x+y)- (x² +y² – 1) and solve =0. дх ду дл 7e 7e 7e %3D
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- Write down the Lagrangian, and hence find the two stationary points of the problem below and Find the Bordered Hessian for this problem, evaluate the required leading principalminors for both solutions. Hence show that one solution is a local maximum and the other is indefinite.Consider the ODE eigenvalue problem: ((1-x2)1/2φ')' + λ(1-x2)-1/2φ = 0 posed for -1 < x < 1 and subject to the boundary condidiont |φ(-1)| < ∞ and |φ(1)| < ∞. If you find it helpful you, you may assume |φ'(-1)| < ∞ and |φ'(1)| < ∞. a) Show that this is a Sturm-Liouville eigenvalue problem, i.e, verify that it has the correct form and identify the coefficients p, q, and σ. Is the problem regular? Why or why not? b) Show that λ > 0 for each eigenvalue λ.In the following problem apply the eigenvalue method to find a general solution of the given system. If initial values are given, find also the corresponding particular solution. use a computer system or graphingcalculator to construct a direction field and typical solutioncurves for the given system. x'1 = 4x1 + x2, x'2 = 6x1 - x2