Find the power series solution for the differential equation $y'' + 3xy' - y = 0$ with the initial conditions $y(0) = 2$ and $y'(0) = 0$. A. $y = x^2 + \frac{5}{12}x^4 + \frac{11}{72}x^6 + ...$ B. $y = x^2 - \frac{5}{12}x^4 + \frac{11}{72}x^6 + ...$ C. $y = 2 + x^2 + \frac{5}{12}x^4 + \frac{11}{72}x^6 + ...$ D. $y = 2 + x^2 - \frac{5}{12}x^4 + \frac{11}{72}x^6 + ...$
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The given differential equation is y + 3xy' - y = 0. We can rewrite it as: 3xy' = 0. Show more…
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