8_HW - 1 . . . 1- = )0( y , 2 = )0(y ; t e4 = y + y2 + y...

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Math 2233 Homework Set 8 1. Determine the lower bound for the radius of convergence of series solutions about each given point x o . (a) y +4 y +6 xy =0, x 0 =0 (b) ( x - 1) y + xy xy x 0 =4 (c) ( 4+ x 2 ) y xy + y x 0 (d) ( 1+ x 2 ) y xy + y x 0 =2 2. Determine the singular points of the following differential equations and state whether they are regular or irregular singular points. (a) xy +(1 - x ) y + xy (b) x 2 (1 - x ) 2 y +2 xy y (c) (1 - x 2 ) 2 y + x (1 - x ) y +(1+ x ) y 3. Compute the Laplace transform of the following functions. (a) f ( t )= t (b) f ( t t n 4. Use the Laplace transform to solve the given initial value problem.
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