4601HW1p2016 - Longman Homework No 1 EEME E4601 Give the...

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Longman’ Homework No. 1 EEME E4601 Give’the’general’solution’of’the’following’homogenous’differential’equations’in’ terms’of’real’valued’functions. Find’the’solution’satisfying’y(0)=1,’dy(0)/dt=0 10.’Find’the’solution’of’
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11.’Follow’the’development’ given’in’class:’Give’the’general’solution’of’ ’ ’ Then’find’values’of’ α ’and’ β ’so’that’the’solution’of’the’following’difference’ equation’can’be’the’same’at’every’sample’time y (( k + 2) k ) + y (( k + 1) k ) + y ( k ) = 0 To’complete’this’match,’we’have’to’find’the’initial’conditions’for’the’second’ equation’that’correspond’to’the’initial’conditions’of’the’original’differential’ equation.’ (1)’If’ y (0) = y 0 ’and’ dy (0) / dt = y 0 ,’find’i nitial’conditions’ y ( kT )’and’ y (( k + 1 ) T )’for’ k =0’
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