Expression 30: "y" "e" Superscript, "H" left parenthesis, "x" , right parenthesis , Baseline equals Start integral from 0 to "x" , end integral, "e" Superscript, "H" left parenthesis, "t" , right parenthesis , Baseline times "g" left parenthesis, "t" , right parenthesis "d" "t" plus "C"yeHx=∫x0eHt·gtdt+C
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Expression 31: "y" equals StartFraction, Start integral from 0 to "x" , end integral, "e" Superscript, "H" left parenthesis, "t" , right parenthesis , Baseline times "g" left parenthesis, "t" , right parenthesis "d" "t" plus "C" Over "e" Superscript, "H" left parenthesis, "x" , right parenthesis , Baseline , EndFractiony=∫x0eHt·gtdt+CeHx
31
Expression 32: "y" equals StartFraction, Start integral from 0 to "x" , end integral, 2 times "e" Superscript, negative 2 "t" , Baseline "d" "t" plus "C" Over "e" Superscript, negative 2 "x" , Baseline , EndFractiony=∫x02·e−2tdt+Ce−2x
32
Den indre funktion
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Expression 34: "u" equals negative 2 "x"u=−2x
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differentieres:
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Expression 36: StartFraction, "d" Over "d" "x" , EndFraction "u" equals negative 2ddxu=−2
36
og dx isoleres:
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Expression 38: "d" "x" equals negative 1 half "d" "u"dx=−12du
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hvorefter u og dx indsættes:
39
Expression 40: left bracket, 2 times "e" Superscript, "u" , Baseline times left parenthesis, negative 1 half , right parenthesis , right bracket "d" "u"2·eu·−12du
40
Expression 41: left bracket, negative 1 times "e" Superscript, "u" , Baseline , right bracket "d" "u" equals negative "e" Superscript, negative 2 "x" , Baseline−1·eudu=−e−2x
Expression 43: "y" equals StartFraction, negative "e" Superscript, negative 2 "x" , Baseline plus "C" Over "e" Superscript, negative 2 "x" , Baseline , EndFractiony=−e−2x+Ce−2x
43
Expression 44: "y" equals "e" Superscript, 2 "x" , Baseline times left parenthesis, negative "e" Superscript, negative 2 "x" , Baseline plus "C" , right parenthesisy=e2x·−e−2x+C
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Expression 45: "y" equals negative "e" Superscript, negative 2 "x" plus 2 "x" , Baseline plus "C" "e" Superscript, 2 "x" , Baseliney=−e−2x+2x+Ce2x
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Expression 46: "y" equals "C" "e" Superscript, 2 "x" , Baseline minus 1y=Ce2x−1