1. The document presents equations for several related differential equations involving functions of x (f(x), g(x), etc.) and their derivatives. 2. The equations contain common functions like exponentials, logarithms, trigonometric functions, and their derivatives. 3. Boundary conditions or initial conditions are provided for solving some of the differential equations.

1. E.rb 1' -- %o"^"" Oioic^rial
1 . ?*t^,^^o^ l*krc,r.sial i^i$ orAe 5a4't
"
@t'-ji -- 4e?"
?G7 = -1 p'*
oC,.) = 4e7*
i
J =e
-f,-rdr
Letrt^* ^ 4gr* Arr+fl
=eex Ugo" .Llgr* a"+d
:(r- (4 Ja"+c)
= e7* ( 14 y+L)
J= 4*ev + c'e3"
&' :'-zx = as ix
PCx)> -2
AU)=Lo5€x
I = €r"fj e.'" . Co5Cu
^*
*{
: fft$,C, (- btex+ frt^ e.)*")
:* (rusrr I rri^a*)Oauz*
@ '-'J = 6e"
?(x):-5
o(.<) z 68*
X =€t.Lteo ,ffa*+l
=et*
(*ne'"* +r)
=hrx 4Ceq*
@v'-?f,= $in a{x
PCxl = -7
&Cr)' 5i"4r
.5=€oS
e+* Ai^ a"a$+l
= et,.ffi, (?rr^ 4 x -4 co5 LIx)+A
= h
(-yqi^A,:-4 ur Ltx) tce?*

2. 2- @. J'+ )'=Cxtt)', J= , 5*- )<=o
?cx): r
&L"): Cxts)'
t :8-- l|e* cv+s)'a*+']
=C* fe" fcxt<)' +z(-+q)+'3+4
=e-*LB* Lxt +gx+tfl +e]
= b'*Lxtr?) + c.e-*
1: I gaat x=o
X: Cx'+8x+q) +L.?,-*
: t?tc
, C- -l?*t
c: -t6 + ?Ou =
@ t'+aj = e+*, X=0, t=1
t cr): z
e&)--e3*
X =g-r* Ber- g-3"dx +c]
=0-* LSe-* A*+4
=
(-zr (-e -* tc)
> -e'k + c-g-'*
1= 2 l*1 x.=O
1 =-€'* * Le-'*
*= -l +a
C= 2 =p eEL r

3. 3,@. 1"-s 1 + 61 :o
["-ft +6>D
G-: ) Cc-z)>O
t t:J
z=2
t "-p' *'t = ,
f '-2{- )z >O
f ,,2:-,2 ! tEB
J-
=3IzL
I
: l!i,x=,,f =t
:cr ei* +Cra"
=(t?t bJx * C,0" Si,.v
C 5.b"*att'+61=6
ta-24( ttg[= D
Cf t -4) ( r-u>= O
@1"-Lt3'+ 31= o
['-"trtt3=a
,f,,2= 3-.L=ffiz
:4 t ,/*r-
-T-' = 1!-6i:z!3t2
t'=f
tz="f
4 El'-3i' +41= o : [=0,1'--2 t44r ]<so
?b = [=-it -[a =O
Cr-z) 66-t)rd
1=2 Vr.=
/' =zcq.- ! Lze +.1 =drgz* *C.s*
(oo1 1{; x: O.
tt C, g?.*4f.2?.*t O=Cr +L"Et)
l':2i x=o
$' :?l ,O'* n (ze- ? ?=>(;+6.127
Lr l(zzO
?L, )b--o -
*Ct - *z
Ct :z
C , f' Cz =0
z )Lz>0
Cz >-Z
1'Ze'*-H
d=2. tP=,

4. G.:"-2$ t l= O I X =l,tan1'= I !ao( r<:6
Pb:t'*)rtl=o
Cr -r) Cr-r)=o
1,2 >
f, >-CrEx * &>xOY
1 = t a[a, x=0
1 : C, ?" *C"oe
y>Ct 0)
1't 2 , -x:o
L > Cre" *C.e'
x- = Cr C.
)-:t ?(-
)-l zC'
:C.
1= e- fe*
>>e'
l"t61'*$1=o {=z,i':t : x:o
P=0"$8rt6:o
4rtq) Cr+a)=o
.,2 <_Z[
tr>c, e-4* *(rxe-q"
X'=*4qg-4*- 4Go-q*
S"rt X=o 1><4
X = l, e''* +(ry(-q'<
O=CrCo*L.o.9o
O:f,
5^*t t': l x>o
f,': - 4, (te"'*-4cre-"
= -(,( (re'- 4Cre*")
= -a{ C,- 46. C?-)
€ ll^i,r"ti
= Lt >O
-LlC,-4(z>l
- 4ta- 4(,*l
O$"-f '-61 =0 , )=@ J.an t'= rsa*( w=@
Qu -- '-r - G -.a
Ctt) cc+6)=o
t, =3T.r=--z
1= Ctgr* + C.0-r*
t: jC. ei*-2 C" €-t*
5*t x:-0 , 1: o
- o= t,)(. (,)
X'= , 5an4 ).=o
X' :3 Ci e3* -LLzAt-
1 = 3 Lle'-zCu€'
I : J c1-L L,. (,
C, t(.7--6
[xl 3 (,*iQ:O
a|-zLtilr fxr I ij,-ilr=l -
-l'"-1,.,
( , l-[, zo
L, )h=o,
Lr=-€
1=+
C, -- -Lr{
na-1*
Ory^S ^t(art) ttt=o
G= t'-)'+5=0
tr,:. = 3i'
t'tt, : t
"tats
X.C, ?'C,r^* lhe* f in &x
t'=-2 L€'iinlx {>C r€* Cor tx
>O 1d4t {=o
g >A Q' u, zLd * heo s; n t(.0)
O "C'
t'=',v=Q
( :*z {,ao Sin zLo) lz(zgocos4p)
>tL,
LLz=1 p(.-lz
/ =2, e' lin h<
/ =Z r" t Yyl*

5. €@ ."'- r{ y"+ t'+ 6 r =o
?_rtre*rt6=-O
rl -Lr t 6
'[ ? -1 -6 -+
-2-90
6-.) Lr'+r-3)=o
Ct*z;cr-3) (r+r)=o
[,:2, 11 = J, 13
=-l
0
X =C rg>' {- (.>gz* *(g1-,*
?z 0
tr-r) (f. + 1r t-rr)>0
Cr-r) Cr+q) drtr):o
t,=l .fr =-'L1 ,p3:-3
ull
rd
2r
+
6
(i
t
I
x"'+
P+ s
1=o{Sy'-ta
$p-":0
t -t-l
7rz
XG t,e* + Lze-q* kqeo*
6'O 1" -31'+ lJ = 1en
?DL to^,gen :
1"-3x'flx=o
[1-3 r tz :o
Cr-f) Cr-D =O
t,:1,[r=a
P.U - Lrc,.tr{€n..
1ic, er lc'e"
tv^Xgi ?ere46r^ '
x:Ae-'
J'=
-*t-"
!": AC-*
&e-' * G*e--) + z(pa- ) =(
g--
|kC: = 4e-*
6lr=,4
ft =.Ye =h
?tt =Y 1= ?, en
@ 'l':' {'3y"-6r'- B; = 0
It{3t'-6r-B=o
_,lr ) -6 -s
l-r-28+z-Bo
Cr+r) C rl t 2 c- g) :6
Cr+ r) ( r+ar) Cc-z ) =o
h.:-, fz: -4 ,1j.7
I -L,e-* * be-** + (t e.,
-)i" + ??y =D
f*->["+a?=D
r' ? -'j -3 ?* 1 -3-t O
tr-l trr + 3s'-ir - 3) = o
(f*) Cr+l) (r.-j) = 0
f, = 3 , f. -- -3 , fg= E ,1o,, =-ff
1'LE^'*Lre'3"+L.Cos ffi tC,,r <i" -{}x
lwae,le.gon'. n erv ^'.
Y-- Xh t-1P
= LtgY lL,e'" + U
g-*
@ x''
I

6. &:"+&t'=(p5,,a
PDL Uno"rp6gn'
X"+1X':o
ft*ar =p
f(rtile o
fr,t I -ZtVG_
J-
:-alz
-
z
f , --- tt =Pi
["---t -t :-2
?u=Xh=L,*(ne-"
f,=A(-lrs),Y1 Bli,ex
X' =-P ft5i,. }x * l8 co *1
tn -- -a{ fi cas Lx - 46 ii" ?x
F.^Cai fercaero-;
@2" l6x' +)J>2,*
/=/t, )ye
* Lt A C-s L> .49gi n 0x lz LaA gtr pr+19 U d* r Gz 4rtn a:. +tB cot x) >Cof 3a
- t4A *48=r
-44-trf-o
-84= t
h=*
-'{A + 4$: I
- "l ('i t +.{B'l
i t'(g=r
48=t -L
g=b
P?=-) q r* lb gin2x
Pu = ,-
J =J tJ?
= (, Lns,fi Vzsr'^fi I Gb os x) * S; n zx
?b:t'I6r*3=€'*
Cr+D Cr+s) =a
f t12 z'J
- th zL, e-r' ) 0,-iea*
f r5ei ?esca!a+^ i
1=Aygr*
5': A Cx*'+ eu)
fl x . rl R
2' , Aae* +6A*2e."* +
Ato t 34xe* =enZlW* - 92tc_(-
4=)L3
I''= A U'4f +*t) =L, 2-x llzg-3r**r*
"u

7. @ Y"l3 16 si^ n(
Yb=$,,2: *.2i
-.F- I
o Li
3t. i4rCol x+ Ct 5t"x
[.r.5fi ?<rz.obr,^;
J=A Scosx tBfsi^x
X'=-A f gi"x tBt&sx
3":-iACoi.k-Btfiax
-A 5 CoS*-B 55i^ x * hS bsx * 85 5i^x I f,ti',x
l? =o
pr= .1
=3h*5?
'C, Co5 x { d. finx
@.1 '-?U't re )= e o
?: f'-1f { tr= o
Ct *) C r-qJ to
Fr=J Y13=.11
yh=4 (rej* 4Lreqx ,.
.
Sv,59i fQrt-aba*n',
lr A eri -
Y':5Aen'
$" t 2s *gr*
75 Aer* -+ tt"Aet, + z Cne*)= €t
rBAerF'i,ti+.
-ffi t'l '
A=*
ls= *en
) =J+I?
>LreT*+Lren* +&er)