In what way is Bernard Shaw's version different from the original Pygmalian story? difference

The original
story ofwas about a sculptor who fell in love with the...

Solve y''+4y'+3y=0, y(0)=2, y'(0)=-1

We begin the
question by finding the general solution of this second order differential equation. In order to
approach this question we need to find the characteristic equation first: 

The characteristic equation is found as follows: 

`D^2 + 4D + 3 =
0`

Now we apply basic factorization: 

`(D+3) (D+1) =
0`

Now we determine the roots by equating each term to zero: 

`D+ 3 = 0 or D+1= 0`

`D = -3 or D = -1`

From the
above roots we can now find the general solution: 

`y (x) = C_1 e^(-3x) + C_2
e^(-x)`

where: 

`C_1 and C_2` are constants. 

Since we have conditions, y(0) = 2 and y'(0) = 1, we can find the particular solution
and solve for the above constants. 

Let's begin with the first constraint:
y(0) = 2

`y(0) = C_1 e^(-3*0) +C_2 e^(-1*0)` , e^0 = 1

`2
= C_1 + C_2` (equation 1)

Now we use the second constraint y'(0)=1. But first
we must find y'(x)

`y' (x) = -3C_1 e^(-3x) - C_2 e^-x`

`y'(0) = -3 C_1 -C_2` (we know from above e^0 =1)

`-1 = -3C_1 -C_2` 
(equation 2)

We have two unknowns and two equations. We can now add both
equations: 

`2-1 = -3C_1 + C_1 -C_2 +C_2`

`1 = -2
C_1`

`C_1 = -1/2`

Now we can find C_2 from equation
1: 

`C_2 = 2 - 1/2 = 5/2`

Now we have our
constants our particular equation is: 

   

`y(x) = (-1/2)
e^(-3x) + (5/2)e^-x`

 

Summarize the main musical elements of the Renaissance Period, the most important genres and techniques.

Generally speaking, the Renaissance was a
time when people prioritized art and science. Their focus began to shift toward worldly
concerns, and this was reflected in musicpreviously, music had centered around religion and the
church, but during this time, composers wrote secular as well as sacred music. Until about the
16th century, choirs and vocal music were popular, with as many as eight different parts for an
ensemble. Instruments (if there were any) usually played the same notes as the voices. Near the
end of the 16th century, instruments took on a different role as composers began to favor
harmonies, polyphonic texture, and complex rhythms. Examples of instruments from this period
include trumpets, lutes, and viols.

A few examples of dominant genres from
this period are the madigral (polyphonic and usually with at least 3 voices), the motet
(polyphonic), and the chanson (polyphonic and secular).

I highly recommend
the link below for a more technical explanation of the main characteristics of Renaissance
music.

href="https://www.rpfuller.com/gcse/music/renaissance.html">https://www.rpfuller.com/gcse/music/renaissance.html

Does Neoclassicism still influence modern architecture?

kateanswers

Neoclassicism does still influence architecture and will continue to influence the
design and understanding of buildings still to come. Neoclassicism harkens back to the Classical
periods of Greek and Rome, and buildings of this style feature characteristics like columns and
geometric forms. This style of architecture grew out of a reaction or distaste for the excess of
Rococo design, which was rich in detail. In turn, many architectural styles have developed as
interpretations of or reactions to Neoclassical style. 

As an example, let's
consider a...

href="https://fallingwater.org/">

href="https://www.britannica.com/art/Neoclassicism">https://www.britannica.com/art/Neoclassicism
href="https://www.metmuseum.org/toah/hd/neoc_1/hd_neoc_1.htm">https://www.metmuseum.org/toah/hd/neoc_1/hd_neoc_1.htm]]>

To what extent is the title of "Hunting Snake" appropriate?

There is a sense in
which the title of this poem could be viewed as focusing only on a part of the content of the
poem: the poem is just as much about the reaction of the speaker and her companions to the snake
as it is about the snake itself. However, when the poem is analysed in detail, it can be seen
that the title can be read in a number of different ways.

On the one hand,
it clearly relates to the snake as a predator. The description of the snake as it
"quests" through the grass with its "Head down, tongue flickering on the
trail" and hunts smaller prey is one that inspires fear in both the reader and...

In
both "The Road Not Taken" and "Fifteen," the speakers are on the edge of an
adventurous journey in a natural and secluded area--the woods and the "back of the
woods" south of a bridge at the edge of town, respectively. Both speakers become cautious
and do not to venture forth into areas that may prove risky. In contrast, though, at the end of
their narratives, the speaker of Frost's poem expresses a certain self-doubt and incompleteness
while the speaker of Stafford's poem feels self-restoration.

As he takes a
walk, Frost's speaker discovers two enticing lanes in the woods that are
"untrodden,"

                                 
 ...long I stood

And looked down one as far as I could

Stafford's speaker, on the other hand, discovers a running
motorcycle that attracts him with the prospect of a new, exciting adventure. The object at which
he looks assumes a femininity that is seductive:

I
admired all that pulsing gleam, the 
shiny flanks, the demure
headlights
fringed where it lay

Further, the
speaker of "Fifteen" indulges delightedly in his imagination of the adventure that he
can have with this machine, and he even takes it to the road. But as he has "a forward
feeling" and there is a tremble, he changes his mind and returns with the motorcycle to the
place he has found it. "Thinking," he finds the owner, whose hand is bleeding. He
helps the owner to his motorcycle and the other calls him a "good man" and rides
off.

 

Both the bridge where the fifteen-year-old
feels the "forward feeling" but resists it and the point where the two roads
"diverged" and the speaker chooses the one more traveled are junctures in the lives of
the speakers of the two poems. These choices that the speakers have made are for what is real
over that which is imagined. For both speakers there is a sense of loss and a change in
themselves; in contrast, however, Stafford's speaker has grown from his experience, while
Frost's speaker merely reflects that his choice "has made all the difference" to
him.

In The Phantom Tollbooth, what does Milo discover when King Azaz calls for his guests to each give a speech?

Because of the
absurdist nature of the worlds that Milo visits in , he is unprepared for the literal nature
of Dictionopolis, ruled by King Azaz. At a banquet, King Azaz calls for his guests to give
speeches, and Milo, thinking that this is a formal affair, speaks:

"Your Majesty, ladies and gentlemen," started Milo timidly, "I would
like to take this opportunity to sat that in all the--"
(Juster, The
Phantom Tollbooth, Google Books)

King Azaz
cuts him off and allows the other guests to speak. Each pronounces a list of foods, after which
the waiters deliver each guest their own words, which presumably taste like the foods they
describe. Milo protests:

"I didn't know that I was
going to have to eat my own words," objected Milo.
"Of course, of course,
everyone here does," the king grunted. "You should have made a tastier
speech."
(Juster, The Phantom Tollbooth, Google
Books)

The following dialogue is a flurry of puns,
offering "somersault" to improve the flavor and advice to wait for "your just
desserts." Since the kingdom of Dictionopolis is a literal world, everything people say has
meaning, and that meaning is translated into reality. Milo's more subjective view does not yet
understand that everything has a reaction, and every word has real meaning that can affect
others, positively or negatively.

href="https://books.google.com/books?id=kxcXm_Q9csEC&printsec=frontcover&hl=en">https://books.google.com/books?id=kxcXm_Q9csEC&printsec=f...