Question: a. Find y(t) satisfying the initial-value problem 9y'' + 6y' + y = 0, y(0) = 1, y' (0) = 2/3 b. Find real-valued functions

a. Find y(t) satisfying the initial-value problem 9y'' + 6y' + y = 0, y(0) = 1, y' (0) = 2/3

b. Find real-valued functions u1(x) and u2(x) in the general solution u(x) = C1u1(x) + C2u2(x) of the Cauchy-Euler equation

4x^2 u'' + 8xu' + u = 0, x > 0 Find C1 and C2 in the general solution so that u(1) = 0 and u ' (1) = 3 .

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