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Ordinary Diff Eq Exam Review Solutions 118

# Ordinary Diff Eq Exam Review Solutions 118 - Â e 2 t Â± 2...

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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: Â¶ e 2( t Â± 2) Â± e t Â± 2 Â· + h ( t Â± 3) Â¶ e 2( t Â± 3) Â± e t Â± 3 Â· 39. L Â± 1 Â± 1 Â± e Â± 5 s s 2 Â² = L Â± 1 Â± 1 s 2 Â² Â± h ( t Â± 5) L Â± 1 Â± 1 s 2 Â²Â³ Â³ Â³ Â³ t ! t Â± 5 = t Â± h ( t Â± 5) ( t ) j t ! t Â± 5 = t Â± ( t Â± 5) h ( t Â± 5) = ( t if Â² t < 5 ; 5 if t Â³ 5 :...
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