Part 1. Obtain a solution to the following differential equation valid near the origin: 1.] For the given differential equation, x = 0 is a/an: A. Regular point B. Ordinary point C. Regular singular point D. Irregular singular point 2. Which of the following is the correct form for the solution y? 100 A. y = 1 anx-r B. y = Two anxn+r 100 C. y=n=0 anx" y"+3xy' +7y=0 100 D.y = E=1 anx" 3. The indicial equation for the given differential equation is: A.r(r-4)= 0 B. r(2r + 1) = 0 C. r(r-3) = 0 D. None of these/Not applicable 4. The recurrence relation for n ≥ 2 is: A. n(n-1)an + (3n+ 1)an-2 = 0 B. n(n-1)an + (3n+7)an-2 = 0 C. n(n+1)an-2 + (3n+ 1)an = 0 D. n(n+1)an-2 + (3n+7)an = 0

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