Onboard Note

Recall that y' is the same as (dy)/(dx) . Then in the given problem: (2+x)y'=3y , we may write it as: (2+x) (dy)/(dx) = 3y.  This will help to follow the variable separable differential equation in a form of N(y) dy = M(x) dx. To rearrange (2+x) (dy)/(dx) = 3y ,cross-multiply (dx) to the other side: (2+x)dy =3y dx Divide both sides by (2+x) : ((2+x)dy)/(2+x) =(3y dx)/(2+x) dy =(3y dx)/(2+x) Divide both sides by y : (dy )/y=(3y dx)/((2+x)y) (dy)/y=(3dx)/(2+x)  To solve for the general solution of the differential equation, apply direct integration on both sides: int (dy)/y=int (3dx)/(2+x) For the left side, apply the basic integration formula for logarithm:  int (dy)/y= ln|y| For the right side, we may apply the basic integration property: int c*f(x) dx = c int f(x)dx . int (3dx)/(2+x)= 3 int (dx)/(2+x)  Let u =2+x then du= dx The integral becomes: 3 int (dx)/(2+x) = 3 int (du)/u We can now apply the  basic integration formula for logarithm on the integral part: 3 int (du)/u= 3l...

In "The Veldt," Bradbury uses different elements of setting. First of all, he uses time to situate his story in the future. Although Bradbury does not reveal a specific year, we know that the story is set in the future because of the existence of the HappyLife Home. The technical sophistication of this house shows that it does not belong to the current year, or the year that Bradbury published this story. This house, for instance, is capable of taking complete care of the family: This house which clothed and fed and rocked them to sleep and played and sang and was good to them. In addition, the house is so technologically advanced that it can react to the physical movements of the family: Their approach was sensed by a hidden switch and the nursery light turned on when they came within ten feet of it. Similarly, behind them, in the halls, lights went on and off automatically as they left them behind. In the story, Bradbury also uses a number of different geographical settings...

In "Caged Bird," Maya Angelou juxtaposes the ideas of a free bird and a caged bird to show the effects of oppression.  Stanza one focuses on the free bird: A free bird leaps on the back of the wind    and floats downstream    till the current ends and dips his wing in the orange sun rays and dares to claim the sky. In this stanza, Angelou uses metaphors to make the flight of the bird appear less like flying and more like floating. For the free bird, flight is effortless as it rests "on the back of the wind / and floats downstream / till the current ends," as if it is lounging on a raft rather than having to put forth any effort on its own. For the free bird, flight is natural and easy. Near the end of the stanza, the rays of the sun are compared to a liquid, which the bird leisurely dips his wings in as he "dares to claim the sky."The progression continues when Angelou returns to the free bird in stanza four: The free bird thinks of another breeze and the ...

According to David Howard-Pitney, author of Martin Luther King, Jr., Malcolm X, and the Civil Rights Struggle of the 1950s and 1960s, King and Malcolm X were moving towards an appreciation of each other's positions towards the end of their lives. They only met each other once—in 1964, when they were both in Washington, D.C. to hear the debate in the Senate on the Civil Rights bill. In 1964, Malcolm X broke away from the Nation of Islam, and he became interested in making connections with civil rights leaders. His travels in Mecca in 1964 caused him to think differently about being a Muslim, as he saw Muslims who were international and interracial in make up, and he increasingly responded to Islam's call for peace. Though he never officially renounced violence or Islam, he had founded a political group called The Organization of Afro-American Unity and was interested in working with civil rights leaders. King in particular commanded his respect as a person and as a leader, and h...

This is a difficult question, and the answer depends in part upon the experience and sensitivity of the reader. Consequently, two different readers may have two different thoughts on the matter. Since you ask for personal thoughts, I will feel free to state my personal thoughts as being that Hill has varying success in producing a female voice for Aminata. In the opening paragraphs, the voice is dominantly male even though there are key words and phrases that are intended to suggest a female mental orientation and a female narrator through such things as a reference to cooking and a simile employing food: "stew of chicken necks ... in the iron pot" and "like pumpkin mush." While the accumulation of key words and phrases, such as "our shared moments had grown like corn stalks in damp soil," point to a female character (as does the feminine ending on the name Aminata), it is not until Aminata actually speaks with the girl at the school that the voice Hill pr...

Federal regulations are rules and standards that have been adopted by certain administrative agencies; they are not laws, but they certainly have had a considerable impact upon all American citizens. These many regulations are published in the Federal Register which is structured into 50 subject matter titles. Among the many government regulations, there are those that protect the safety of workers, such as automation hazards and biohazards [Federal Occupational Safety and Health Administration (OSHA) regulations], and others that cover other important facets of life. Environmental regulations ensure that water is cleaner and other natural resources are obtained in ways that are safe to the environment. Still other regulations cover such areas as travel, manufactured products, and banking. In a report of the top ten industries that are under federal regulation, these are included (Note: The numbers that follow the industry-relevant restrictions provided are divided by 1,000 for ease of...

In Chapter 6, "An Exquisite of '92," from The Scarlet Pimpernel, Marguerite becomes increasingly dismayed about her brother's return to France. She has so enjoyed his visit to her home in England, especially because of her husband's now distant and cold relationship with her. As she prepares to say goodbye to her only kin, she is troubled by the merry nature of Sir Percy and his band of friends and asks to be able to say farewell in private. At the end of the chapter, as Sir Percy silently admires the loyal bond between his new wife and her brother, he provides readers with the surface reason for Armand's return to France. Sir Percy observes that Marguerite's "love for her brother, Armand St. Just, was deep and touching in the extreme. He had just spent a few weeks with her in her English home, and was going back to serve his country, at the moment when death was the usual reward for the most enduring devotion." Even though Armand's cause—at ...