MA2132 - HW03

# MA2132 - HW03 - Willis Thai MA2132 Worksheet 3 1 Find the...

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MA2132 – Worksheet 3 1. Find the solution of the IVP 0 5 2 = + y y y , 1 ) 0 ( = y , 1 ) 0 ( = y . ) 2 cos( ) ( 0 2 1 1 ) 0 ( ) 2 cos( 2 ) 2 sin( ) 2 sin( 2 ) 2 cos( ) 2 sin( ) 2 cos( ) 0 sin( ) 0 cos( 1 ) 0 ( ) 2 sin( ) 2 cos( ) sin( ) cos( 2 1 2 1 2 16 2 2 4 0 5 2 2 2 2 2 2 1 0 2 0 1 2 1 2 1 2 2 t e t y C C y t e C t e C t e t e y t e C t e y C e C e C y t e C t e C y t e C t e C y i r i a ac b b r r r t t t t t t t t t t t = = + = = + + = + = = + = = + = + = = = ± = ± = ± = ± = = + β α 2. Consider the homogeneous, second order linear ODE 0 3 2 = y y t y t , 0 > t . a. Use the substitution r t y = to find solutions 1 y and 2 y . 1 2 3 1 2 1 2 2 2 2 1 1 , 3 0 ) 1 )( 3 ( 0 ) 3 2 ( 0 3 ) ( ) ( = = = = = + = = = = = t y t y r r r r t r r t t rt t r r t r r y rt y t y r r r r r r r r b. Use the Wronskian to verify that 1 y y and 2 y are linearly independent.

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MA2132 - HW03 - Willis Thai MA2132 Worksheet 3 1 Find the...

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