hw2 - a mn x 2 m x 2 n + 1 + x = , x ( ) = 1 , x ( ) = ,...

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MAE294B/SIO203B: Methods in Applied Mechanics Winter Quarter 2010 http://maecourses.ucsd.edu/mae294b Homework II Due January 21, 2010. 1 Find the values of α for which solutions to the equation ¨ x +( 1 + 4 ε cos α t ) x = 0 , 0 < ε ± 1 have increasing amplitude for ε t = O ( 1 ) . 2 Find a solution uniformly valid for ε t = O ( 1 ) to the equation ¨ x + x + e - ε ˙ x 3 = 0 , x ( 0 ) = 1 , ˙ x ( 0 ) = 0 , 0 < ε ± 1 . 3 Find the values of the 6 real coefficients a 00 , a 01 , a 10 , a 20 , a 11 and a 02 for which the equation ¨ x + m 0 , n 0 , m + n 2
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Unformatted text preview: a mn x 2 m x 2 n + 1 + x = , x ( ) = 1 , x ( ) = , &lt; 1 has a periodic solution for t = O ( 1 ) . What is the role of initial conditions? 4 Find solutions uniformly valid for t = O ( 1 ) to the equation x + x- ( x-x 2 ) = , x ( ) = 1 , x ( ) = a , &lt; 1 . What happens when a =-1? 1...
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