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Unformatted text preview: x = 2. 2 y 00 + ( x + 1) y + 3 y = 0 , y (2) =3 , y (2) = 1 . 4 5. Determine a lower bound for the radius of convergence of series solutions about each given point x for the following diﬀerential equation. ( x 22 x3) y 00 + xy + 4 y = 0; x = 4 , x =4 , x = 0 . 5 6. Consider the Euler equation x 2 y 00 + αxy + βy = 0. Find conditions on α and β so that: (a) All solutions approach zero as x → 0. (b) All solutions approach zero as x → ∞ . 6 7. Find all singular points of the following diﬀerential equation and determine whether each one is regular or irregular. ( x sin x ) y 00 + 3 y + xy = 0 . 7 8. Seek a power series solution of the following diﬀerential equation about the given point x = 0. 2 xy 00 + y + xy = 0 . 8...
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 Spring '08
 Fonken
 Calculus, Power Series, Mass, Englishlanguage films, Complex number, Radius of convergence

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