first order linear ordinary difernetial equation...SO I.F.=e^-.pdf

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This document discusses the solution to a first order linear ordinary differential equation. The integrating factor is e^-x. The solution is given as y=c1e^-x + x^-1, where c1 is a constant.

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first order linear ordinary difernetial equation...
SO I.F.=e^-x
Solution
y=c1e^-x+x^-1

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The start of the European Colonization is typically dated to 1492, although there was at least one earlier colonization effort. The first known Europeans to reach the Americas are believed to have been the Vikings (\"Norse\") during the eleventh century, who established several colonies in Greenland and one short-lived settlement at L\'Anse aux Meadows in the area the Norse called Vinland, present day Newfoundland. Settlements in Greenland survived for several centuries, during which time the Greenland Norse and theInuit people experienced mostly hostile contact. By the end of the fifteenth century, the Norse Greenland settlements had collapsed. In 1492, a Spanish expedition headed by Christopher Columbus reached the Americas, after which European exploration and colonization rapidly expanded, first through much of the Caribbean region (including the islands of Hispaniola,Puerto Rico, and Cuba) and, early in the sixteenth century, parts of the mainlands of North and South America. Eventually, the entire Western Hemisphere would come under the domination of European nations, leading to profound changes to its landscape, population, and plant and animal life. In the nineteenth century alone over 50 million people left Europe for the Americas. The post-1492 era is known as the period of the Columbian Exchange. The potato, the pineapple, theturkey, dahlias, sunflowers, magnolias, maize, chilies, and chocolate went East across theAtlantic Ocean. Smallpox and measles but also the horse and the gun traveled West. The flow of benefit appears to have been one-sided, with Europe gaining more. However, the colonization and exploration of the Americas also transformed the world, eventually adding 31 newnation-states to the global community. On the one hand, the cultural and religious arrogance that led settlers to deny anything of value in pre-Columbian America was destructive, even genocidal. On the other hand, many of those who settled in the New World were also social and political visionaries, who found opportunities there, on what for them was a tabula rasa, to aim at achieving their highest ideals of justice, equality, and freedom. Some of the world\'s most stable democraciesexist as a result of this transformative process. The first conquests were made by the Spanish and the Portuguese. In the 1494 Treaty of Tordesillas, ratified by the Pope, these two kingdoms divided the entire non-European world between themselves, with a line drawn through South America. Based on this Treaty, and the claims by Spanish explorer Vasco Núñez de Balboa to all lands touching the Pacific Ocean, the Spanish rapidly conquered territory, overthrowing the Aztec and Inca Empires to gain control of much of western South America, Central America, and Mexico by the mid-sixteenth century, in addition to its earlier Caribbean conquests. Over this same time frame, Portugalconquered much of eastern South America, naming it Brazil. Early conquests, claims, and colonies Other Eur.

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