Ordinary Diff Eq Exam Review Solutions 118

Ordinary Diff Eq Exam Review Solutions 118 - e 2( t 2) e t...

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120 1 Solutions 35. L ± 1 ± e ± 2 s s 2 + 4 ² = h ( t ± 2) L ± 1 ± 1 s 2 + 4 ²³ ³ ³ ³ t ! t ± 2 = h ( t ± 2) ( 1 2 sin 2 t ) ³ ³ t ! t ± 2 = 1 2 h ( t ± 2) sin 2( t ± 2) = ( 0 if 0 ² t < 2 ; 1 2 sin 2( t ± 2) if t ³ 2 : 36. L ± 1 ± e ± 2 s s 2 ± 4 ² = h ( t ± 2) L ± 1 ± 1 s 2 ± 4 ²³ ³ ³ ³ t ! t ± 2 = h ( t ± 2) L ± 1 ± 1 4 ´ 1 s ± 2 ± 1 s + 2 µ²³ ³ ³ ³ t ! t ± 2 = h ( t ± 2) ( 1 4 ( e 2 t ± e ± 2 t ) ³ ³ t ! t ± 2 = 1 4 h ( t ± 2) e 2( t ± 2) ± e ± 2( t ± 2) · = ( 0 if 0 ² t < 2 ; 1 4 e 2( t ± 2) ± e ± 2( t ± 2) · if t ³ 2 : 37. L ± 1 ± se ± 4 s s 2 + 3 s + 2 ² = h ( t ± 4) L ± 1 ± s s 2 + 3 s + 2 ²³ ³ ³ ³ t ! t ± 4 = h ( t ± 4) L ± 1 ± 2 s + 2 ± 1 s + 1 ²³ ³ ³ ³ t ! t ± 4 = h ( t ± 4) (2 e ± 2 t ± e ± t ) ³ ³ t ! t ± 4 = h ( t ± 4) 2 e ± 2( t ± 4) ± e ± ( t ± 4) · = ( 0 if 0 ² t < 4 ; 2 e ± 2( t ± 4) ± e ± ( t ± 4) if t ³ 4 : 38. L ± 1 ± e ± 2 s + e ± 3 s s 2 ± 3 s + 2 ² = h ( t ± 2) L ± 1 ± 1 s 2 ± 3 s + 2 ²³ ³ ³ ³ t ! t ± 2 + h ( t ± 3) L ± 1 ± 1 s 2 ± 3 s + 2 ²³ ³ ³ ³ t ! t ± 3 = h ( t ± 2) L ± 1 ± 1 s ± 2 ± 1 s ± 1 ²³ ³ ³ ³ t ! t ± 2 + h ( t ± 3) L ± 1 ± 1 s ± 2 ± 1 s ± 1 ²³ ³ ³ ³ t ! t ± 3 = h ( t ± 2) ( e 2 t ± e t ) ³ ³ t ! t ± 2 + h ( t ± 3) ( e 2 t ± e t ) ³ ³ t ! t ± 3 = h ( t ± 2)
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Unformatted text preview: e 2( t 2) e t 2 + h ( t 3) e 2( t 3) e t 3 39. L 1 1 e 5 s s 2 = L 1 1 s 2 h ( t 5) L 1 1 s 2 t ! t 5 = t h ( t 5) ( t ) j t ! t 5 = t ( t 5) h ( t 5) = ( t if t &lt; 5 ; 5 if t 5 :...
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