Ejercicios de repaso sección 3.9

Resolver la ED de orden superior por Cauchy Euler.

  1. x2y′′−2y=0\hspace{0.5cm}x^2y''-2y=0

  1. xy′′−3y′=0\hspace{0.5cm}xy''-3y'=0

  1. x2y′′+xy′+4y=0\hspace{0.5cm}x^2y''+xy'+4y=0

  1. x2y′′−3xy′−2y=0\hspace{0.5cm}x^2y''-3xy'-2y=0

  1. 4x2y′′+4xy′−y=0\hspace{0.5cm}4x^2y''+4xy'-y=0

  1. x2y′′+5xy′+4y=0\hspace{0.5cm}x^2y''+5xy'+4y=0

  1. x2y′′−7xy′+41y=0\hspace{0.5cm}x^2y''-7xy'+41y=0

  1. x3y′′′−6y=0\hspace{0.5cm}x^3y'''-6y=0

  1. x3y′′′+xy′−y=0\hspace{0.5cm}x^3y'''+xy'-y=0

  1. xy(4)+6y′′′=0\hspace{0.5cm}xy^{(4)}+6y'''=0

  1. xy′′−4y′=x4\hspace{0.5cm}xy''-4y'=x^4

  1. 2x2y′′+5xy′+y=x2−x\hspace{0.5cm}2x^2y''+5xy'+y=x^2-x

  1. x2y′′−xy′+y=2x\hspace{0.5cm}x^2y''-xy'+y=2x

  1. x2y′′−2xy′+2y=x4ex\hspace{0.5cm}x^2y''-2xy'+2y=x^4e^x

  1. x2y′′+xy′−y=ln⁡∣x∣\hspace{0.5cm}x^2y''+xy'-y=\ln \left| x\right|