Answer:An initial condition is an extra bit of information about a differential equation that tells you the value of the function at a particular point. Differential equations with initial conditions are commonly called initial value problems.
The video above uses the example
{
d
y
d
x
=
cos
(
x
)
y
(
0
)
=
−
1
to illustrate a simple initial value problem. Solving the differential equation without the initial condition gives you
y
=
sin
(
x
)
+
C
.
Once you get the general solution, you can use the initial value to find a particular solution which satisfies the problem. In this case, plugging in
0
for
x
and
−
1
for
y
gives us
−
1
=
C
, meaning that the particular solution must be
y
=
sin
(
x
)
−
1
.
So the general way to solve initial value problems is: - First, find the general solution while ignoring the initial condition. - Then, use the initial condition to plug in values and find a particular solution.
Two additional things to keep in mind: First, the initial value doesn't necessarily have to just be
y
-values. Higher-order equations might have an initial value for both
y
and
y
′
, for example.
Second, an initial value problem doesn't always have a unique solution. It's possible for an initial value problem to have multiple solutions, or even no solution at all.
Explanation:
Answer:
To begin, select the shapes you want to format. To select more than one, press and hold the Shift key. When you select one or more shapes, a new Drawing Tools tab appears. Here, you can select Shape Fill to fill the selected shapes with a solid color, gradient, texture, or picture.
Explanation:
Answer:
4160000 bytes
Explanation:
One page = 52 lines of text
One line of text = 80 characters
=> One page = 80 x 52 = 4160 characters
Therefore, 500 pages of text will have 4160 x 500 characters = 2080000 characters.
Since 1 character takes up 2 bytes of computer memory, it impleies that a 500 page novel will take up 2080000 x 2 bytes = 4160000 bytes.
Answer:
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