Question: The problems in this section will give some practice using power series to solve differential equations. 3. For each of the following differential equations: i.

The problems in this section will give some
The problems in this section will give some practice using power series to solve differential equations. 3. For each of the following differential equations: i. Seek power series solutions of the given differential equation about the given point To; find the recurrence relation that the coefficients must satisfy. ii. Find the first four nonzero terms in each of two solutions y1 and y2 (unless the series terminates sooner). iii. By evaluating the Wronskian W[y1, #2](ro), show that y1 and yz form a fundamental set of solutions. iv. If possible, find the general term in each solution. (a) y" - ry' - y =0, TO = 0 (b) my" ty' try =0. TO = 1 (c) 2y" + (x + 1)y' + 3y = 0, CO = 2

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