Question: 14. Using a power series centered at x = 0, solve the equation (x + 1)y + (x + 2)y' - y = 0. State

14. Using a power series centered at x = 0, solve the equation (x + 1)y" + (x + 2)y' - y = 0. State the recursive formula and show the first 4 non-zero terms of each independent solution. (8 pts) 15. For the non-linear differential equation: dy V2 (x - 1)2 1 dx 9 4 (a) Use a computer algebra system (CAS) to generate a slope field for the DE, and attach a printout of the result. (4 pts) (b) Analyze the slope field to determine the equation of the tangent line to y (x) when y(-1) = 1. (2 pts)

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