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ECUACIONES DIFERENCIALES
UNIVERSIDAD NACIONAL ABIERTA Y A DISTANCIA UNAD
ESCUELA DE CIENCIAS AGRICOLAS, PECUARIAS Y DEL MEDIO AMBIENTE
ACTIVIDAD_ TRABAJO COLABORATIVO 2_APORTE
PROGRAMA INGENIERIA AMBIENTAL
GRUPO_ 100412_235
PRESENTADO A:HECTOR IVAN BLANCO (TUTOR)
PRESENTADO POR:
DENNIS ANDREA HERNANDEZ
C.C_ 52499189
SHEYLA PAOLA BUENAÑOS
CC 52335751
30 DE MARZO DE 2015
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CEAD-AG
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TRABAO A DESARROLLAR- INDIVIDUAL
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EERCICIOS
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A. x dy
dx+ x3
y=0
B. y2 x
' +2 yx=0
C. HE:LA BUENA;O
D.
E. DENNI HERNANDE<
=. DENNI HERNANDE<
>. y' − yx=5 x
H. xy' + y=5 x
2
I. x2 y ' +3 xy=
senx
x
2! D"-s'## 6+" / ? s, s%+c&,"s %&,"%-",'" &,$"*",$&",'"s $" % s&!+&",'"
"c+c&@, $&0"#",c&%
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3! . R"s%"# % s&!+&",'" "c+c&@, $&0"#",c&% *# "% -'$ $" #&c&@, $" *#-"'#s
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x2 y
' ' − xy+ y=04 x ln( x )
. R"s%"# %s s&!+&",'"s "c+c&,"s $&0"#",c&%"s *# "% -'$ $" c"0&c&",'"s&,$"'"#-&,$s
y'' 2 y
' +5 y=24 e3 x
"! E,c,'## +, *"#$# $&0"#",c&% 6+" ,+%" '"%% R$#!+"
. x+3 xye6 x
. ( x3−2 x)( x2−1)
c.
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5! R"s%"# % s&!+&",'" "c+c&@, $&0"#",c&% DENNI HERNANDE<
=&,%-",'"
R"%&# % *#+" '&* '"s' c, "% 0&, $" "%+# %s ,c"s $" s+ *#c"s
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SOLUCION
TEM#TICA: ECUACIONES DIFERENCIALES DE ORDEN SUPERIOR
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C. R"s%"#
/ / / F
B+sc-s s%+c&,"s $" % 0#-
/ " #'
A# s" c%c+%, %s $"#&$s
/ #" #' / # 2 " #'
+s'&'+/",$ ", % "c+c&@, $&0"#",c&% $
# 2 " #' (#" #' ) (" #' )
(R 2 # ) " #' F
A% $&&$&# *# " #' s" '&","
# 2 # F
(R 3) (# G 2) F
P$"-s c,c%+&# 6+" $s s%+c&,"s s,
/ 1 " 3' / / 2 " 2'
P$"-s c,c%+&# 6+"
/ c 1 " 3' G c 2 " 2'
E!
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Ec+c&@, %&,"% , -!," c, c"0&c&",'"s c,s','"s.
m2−9=0
(m−3 )2=0→m1=3 y m
2=−3
m1≠m2
T&"," $s #c"s #"%"s $&s'&,'s. L s%+c&@, !","#% "s
y=c1 e3 x+c2e
−3 x
A#
y p=B
y ' p=0
y ' ' p=0
R""-*%-s %s $"#&$s $" % "c+c&@, !","#%
y ' ' −9 y=54
0−9B=54
B= 54
−9=−6
R""-*%-s "% %# $" ", % "c+c&@, / *
y p=−6
A# #""-*%-s %s %#"s $" / / / * ", /
/ / G / *
P# ',' % s%+c&@, "s
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y=c1 e3 x+c2e
−3 x−6
F!
Ec+c&@, , %&,"% -!," c, c"0&c&",'"s c,s','"s
S$%&'()*:
L "c+c&@, c#c'"#s'&c
m
2
+25
=0
m2=−25→m=√ −25
m≠∓5 i
T&"," #c"s c-*%"s. L s%+c&@, !","#% "s
yh=c1 e0 xcos5 x+c2 e
0 xsen5 x
yh=c1cos5
x+c2 sen5 x
A#
y p=asenx
y ' p=acosx
y ' ' p=−asenx
R""-*%-s %s $"#&$s ", % "c+c&@,
y' ' +25 y=6 senx
−asenx+25 (asenx )=6 senx
senx+(−a+25a )=6 senx
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−a+25a=6 senx
senx
24a=6
a= 624
=14
R""-*%-s "% %# $" B ", % "c+c&@, $" / *
y p=1
4 senx
R""-*%-s %s %#"s $" / / / * ", /
y= yh+ y p
P# % ',' % "c+c&@, "s
y=c1cos5 x+c
2sen5 x+
1
4 senx
y=c1cos5 x+c
2sen5 x+
senx
4
4. E,c,'## +, *"#$# $&0"#",c&% 6+" ,+%"
. ( x3−2 x)( x2−1)
R"%&-s % *"#c&@,
x6− x3−2 x
3+2 x
O*"#$# ,+%$# "s D7 *#6+" "% -/# "*,",'" "s / s" %" s+- 1
I!+%-s D
D= x6− x3−2 x3+2 x
I,'"!#-s % *#&-"# "
D1=6 x
5−3 x2−6 x
2+2
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I,'"!#-s % s"!+,$ "
D2=30 x
4−6 x−12 xI,'"!#-s % '"#c"# "
D3=120 x3−6−12
I,'"!#-s % c+#' "
D4=360 x
2
I,'"!#-s % 6+&,' "
D5=720 x
I,'"!#-s % s"' "
D
6
=720
I,'"!#-s % s*'&- "
D7=0
$.
O*"#$# ,+%$# "s D4 *#6+" "% -/# "*,",'" "s 3 / s" %" s+- 1
I!+%-s D / #$"-,s
D=8 x3−5 x
2+1I,'"!#-s % *#&-"# "
D1=24 x
2−10 xI,'"!#-s % s"!+,$ "
D2=48 x−10
I,'"!#-s % '"#c"# "
D3=48
I,'"!#-s % c+#' "
D4=0
5!
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R"s%"# % s&!+&",'" "c+c&@, $&0"#",c&%
R"s%"#"-s +'&%&,$ % "c+c&@, c+c/ "+%%"# s+-&-s +, s%+c&@, $" % 0#- /
y= xm
y ' =m xm−1
y ' ' =m(m−1) xm−2
x2 [m(m−1) xm−2 ]+ x (mx
m−1 )+ xm=0
m (m−1 ) xm+mxm+ x
m=0
xm¿
m (m−1 )+m+1=0
xm¿
m2−m+m+1=0
xm¿
xm(m2+1)=0
C%c+%-s %s #c"s
m2+1=0
m=−0±√ −0−4
2
2
m1.2=±2i
L s%+c&@, !","#% *# 2 #c"s c-*%"s c,+!$s s"#&
y=c1cos (2ln ( x ) )+c2
sen (2 ln ( x ) )
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REFERENCIAS BIBLIOGRAFICAS
1 AIME ESCOBARA! ECUACIONES DIFERENCIALESCON APLICACIONES EN MAPLE. P#0"s# '&'+%# $" % U,&"#s&$$ $" A,'&6+& ( P!s. 7 389) A#c& PD= U%'&-c,s+%' #"%&$ "% 3F $" K# $" 2F15 #"c+*"#$ $"''*-'"-'&cs.+$"."$+.cM"sc#$cs%&#ED.*$0
2 JUAN LUI VARONA KALUKBRE. P#0"s# $"% D"*#'-",' $" K'"-'&cs /C-*+'c&@, $" % U,&"#s&$$ $" L R& (199). METODOS CLASICOS DE
RESOLUCION DE ECUACIONES DIFERENCIALES ORDINARIAS ( Es* 34F1)UNIVERIDAD DE LA RIOJA A#c& PD= U%'&- c,s+%' #"%&$ "% 3F $" K# $"2F15 #"c+*"#$ $" ''*.+,&#&."sc+#,$,%$sL&#ED.*$0
3 P+#c"%% E.J V#"#! D. R&!$, .E. (2FF7). C%c+% K&c_ P"#s, E$+cc&@,A#c& PD= %'&- c,s+%' "% 3F $" K# $" 2F15. R"c+*"#$.
4 RONDON DURAN J. E. (2F1F). Modulo cálculo integral. (B!' C%-&). A#c&PD= %'&- c,s+%' "% 17 $" K# $" 2F15. R"c+*"#$.
5 CAKPO B. CHIRALT C. (2F11). Ec+c&,"s $&0"#",c&%"s. D"*#'-",' $"K'"-'&cs U,&"#s&$$ J+-" I. Cs'"%%@, $" % P%, P+%&cc&,"s $" % U,&"#s&''J+-" I. L""# *!&,s 115 118 IBN 97884939777F U%'&- c,s+%' #"%&$ "% 3F$" K# $" 2F15 #"c+*"#$ $" ''*."',ss0'.c-&%&'"c0+,$-",'s-'"-'&cs$"%&,!",&"#&
CUARTA R. (2F11). K@$+% 4 "c+c&,"s $&0"#",c&%"s $" #$", s+*"#&#. V&$"s.Q%'&- c,s+%' #"%&$ "% 3F $" K# $" 2F15 #"c+*"#$ $"''*+%.'#"s*%+s.c-R"#'C+#'sECUACIONEDI=ERENCIALE
7 ECOBAR J. (2FF4). Ec+c&,"s $&0"#",c&%"s c, *%&cc&,"s ", -*%". L""# *!&,s81 1FF. T"' c-*%"'. Q%'&- c,s+%' #"%&$ "% 3F $" K# $" 2F15 #"c+*"#$ $"''*-'"-'&cs.+$"."$+.cM"sc#