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:
In C++:
int PrintInBinary(int num){
if (num == 0)
return 0;
else
return (num % 2 + 10 * PrintInBinary(num / 2));
}
Explanation:
This defines the PrintInBinary function
int PrintInBinary(int num){
This returns 0 is num is 0 or num has been reduced to 0
<em> if (num == 0) </em>
<em> return 0; </em>
If otherwise, see below for further explanation
<em> else
</em>
<em> return (num % 2 + 10 * PrintInBinary(num / 2));
</em>
}
----------------------------------------------------------------------------------------
num % 2 + 10 * PrintInBinary(num / 2)
The above can be split into:
num % 2 and + 10 * PrintInBinary(num / 2)
Assume num is 35.
num % 2 = 1
10 * PrintInBinary(num / 2) => 10 * PrintInBinary(17)
17 will be passed to the function (recursively).
This process will continue until num is 0
Answer:
C.R.U.D stands for Create, Read, Update, Delete.
Explanation:
Three characteristics of an ideal encrytion scheme are:
1. The encryption sheme should be strong: the algorithm is imprevious to direct attack and attempts are derived.
2. The encryption scheme should create unique ciphertext from the same plaintext for each key permutation, among other traits.
3. It should take at least millions of years to break ideal encryption scheme, based on mathematical predictions.
