oblem #1: Consider the following statements. Problem = 1 (i) Every linear nth order homogeneous ODE has a solution of the form y(x) ex, where r is some real number. (ii) The fundamental set of solutions to y" — 2my' + m²y = 0, where m > 0, is given by {ex.xex for some appropriate real value ₁ > 0. (iii) The auxiliary equation of my" - my' mr mr + k = 0. + ky = 0, where n, m, k are real numbers with n 0, is given by (iv) Consider y"" + ay" + by' + cy = 0 and let 1.2 be two different roots of the polynomial P(r) = 1³ + ar² + br + c. Then the general solution is given by y(x) = c₁e¹¹x + c₂e¹2x (v) Two complex values that are not real solve the auxiliary equation of y" + my' + m²y = 0, where m > 0. Determine which of the above statements are True (1) or False (2). So, for example, if you think that the answers, in the above order, are True False,False. True False, then you would enter '1.2.2.1.2' into the answer box below (without the quotes).

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