19. [-/ 1 Points] 0/6 Submissions Used Find two power series solutions of the given differential equation about the ordinary point \( x=0 \). \[ y^{\prime \prime}-5 x y=0 \] \( y_{1}=1-\frac{5}{6} x^{3}+\frac{5}{36} x^{6}-\ldots \) and \( y_{2}=x-\frac{5}{12} x^{4}+\frac{25}{504} x^{7}-\ldots \) \( y_{1}=1+\frac{5}{2} x^{2}+\frac{25}{24} x^{4}+\ldots \) and \( y_{2}=x+\frac{5}{6} x^{3}+\frac{5}{24} x^{5}+\ldots \) \( y_{1}=1-\frac{5}{2} x^{2}+\frac{25}{24} x^{4}-\ldots \) and \( y_{2}=x-\frac{5}{6} x^{3}+\frac{5}{24} x^{5}-\ldots \) \( y_{1}=1+\frac{5}{6} x^{3}+\frac{5}{36} x^{6}+\ldots \) and \( y_{2}=x+\frac{5}{12} x^{4}+\frac{25}{504} x^{7}+\ldots \) \( y_{1}=1+5 x^{2}+\frac{25}{6} x^{3}+\ldots \) and \( y_{2}=x+5 x^{2}+\frac{25}{12} x^{4}+\ldots \) Resources
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Step 1: Assume a power series solution for \( y \) of the form: \[ y = \sum_{n=0}^{\infty} a_n x^n \] Show more…
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ZILLDIFFEQMODAP10 6.2.015. Find two power series solutions of the given differential equation about the ordinary point x = 0. y'' - (x + 1)y' - y = 0 y1 = 1 + x^4/2 + x^6/6 + x^8/6 + ... and y2 = x + x^3/2 + x^5/2 + x^7/4 + ... y1 = 1 + x^2/2 + x^3/6 + x^4/6 + ... and y2 = x + x^2/2 - x^3/6 - x^4/6 + ... y1 = 1 - x^2/2 - x^3/6 + x^4/12 + ... and y2 = x + x^2/2 - x^3/6 - x^4/6 + ... y1 = 1 + x^2/2 + x^3/6 + x^4/6 + ... and y2 = x + x^2/2 + x^3/2 + x^4/4 + ... y1 = 1 - x^2/2 - x^3/6 + x^4/12 + ... and y2 = x + x^2/2 + x^3/2 + x^4/4 + ...
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