Bolulion - (A) The Linear Homogenous differen tiol Equation of ordes 2 with Ce ficients in the assumed. dange (9, 6) is Both lincarly independent Cincar Soletion y, and y,, this Equation has one and only one To 8how :- Both Cine tool Cet Yoot and yo between two Consecutive seros of 9, and t2 be two Gnsecutive 3eles of 9,lti) = and 9, It2) #o and 9,1tっ) =o ニ6 but o therurise, y, aboul Y2 are Unearly dependent inla, 80, Gee Suppose if is no zer0 of there between A, and tż thun. 9,()も0 de fine the func tion PIA)
Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
its an answer. please typr it i cant read handwritten .
![9, (+) +0
in (8,, t2]
and y,, Y2 are
Con tinuouly differen tiable fanctiond.
9 By Rolle's
t'e (e, ta)
such that-
theorem
W (Y,, Y,; £)
It)
uwither wieh which e
Gnteradic tim
to
assumphing
y, and Ye ls unearly inidepen dent,
that
80, in between
t; and f2
2.
smilarly if we follow the poocess witha Y, aondy,
then
we get
in between any tedo Setetof Griecuhive
seras of Y2
a agero of y,
7 Bero} of 9, and
altandtiuly .
Occ Wrs
(B) Is there
Cineas and
that two. fume tions
and ť-)
Humorgineous eguation
of order 2
wi'th
the
Solulions
et
tincarly
: clearly
independent.
f-1 =0
are
et and f -1
t = 土|
and
R.
4
but
is no zro of er in befeween
and
there
(-1, 1)
Equation of ardes 2 # with Solu tims
Hamoguncaus
Solu tions
g no Cineals
et and](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb0627979-9707-4013-a5be-6977223784b2%2F0b90e7af-4015-4130-b4ee-0365a00f9265%2F31pkfbw_processed.jpeg&w=3840&q=75)
![The linear Momogenous differen tiol
Equation of ordes 2 with CGe fticients in the
assumed.
8o lulion - (A)
Dange
(9,b) is
Both Cincarly indeperdent
y, and y,, this Equalion has one
To 8 how :-
Cincar Solutimes
and only one
aned Yo:
Yoot between two Conseuutive seros of 9,
Cet
and
be two
Consecutive sees
of
im 19,6) 7
9,lt;) =
and 9,1t2) = 0
but
and 9, It2) #o
o therurise, y, atrel y,
Geaee suppose if
are linearly dependent inla,b).
80,
there
is no zero of
A, and tz
thin. 9, It) +o
between
[t,, Az]
de fine
the
fumc tion
PIA)
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