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Please solve questions 4-7, thanks.
Series solution of variable-coefficient ODE Consider the variable coefficient linear second order homogeneous ODE (r² + 1)y" -- Ary | 6y = 0. (1) 2 1. The point = 0 is an ordinary point of equation (1). Therefore, we can find a power series solution of the form. 1702 V- am m=0 Write down the first and second derivatives of the power series. 2 2. Substitute the power series (and its derivatives) into equation (1). Express your answer in the form x 2 4 ΣCm™ = 0, 771() 77 0 where bm and Cm are to be written in terms of m and am. 2 3. Shift the index on one of the series you found in 2 so that the exponents of a are equal to m in both series. 2 4. Find a recurrence relation for the coefficients am 12 in terms of am and m. 4 5. Use the recurrence relation to find expressions for the coefficients a2, a3, a4 and as. 3 6. Write down the general solution to (1) in the form y aof(x) + aig(x). 3 7. Find the particular solution of (1) that satisfies the initial conditions y(0) = 3 and y'(0) = 2.