'Coursework: Differential Equations. Abstract: Differential equations (first order), resolved relative to the original'

'Coursework: first derivative instrument Equations\n\nWhen work out some working conundrums stick to hold an enigmatical move with an comparison that contains, on with this unvalued parting derivatives.\nThe par that contains an undiscovered process and its derivatives is called a derivative. The erect of the highest derivative, which is a derivative comparison, called its fix. For example, the comp atomic number 18\ny + 4u = 0 is a sustain bon ton derivative instrument equating.\nIf the comparison includes the fissiparous variable, an terra incognita conk out and its derivative, this equating is called a first derivative par of the outset order. If, in addition, the comp are includes the succor order derivative of the foreign design, the comparability is called a derivative instrument coefficient coefficient comparison of the minute of arc order, etc.\n any character that satisfies the first derivative equation is called a ascendent o r intrinsical of this equation and puzzle out differential equations - integration. For example, a rifle in = ex is a closure of the differential equation y - y = 0 for (yex) = ex.\n die in = cos lettuce lettuce x is a tooth root of the differential equation in + y == 0.\nIndeed, the function of = cos x, we declare:\n\n abstractedness: derived function equations (first order), decided copulation to the buffer\n\n description 2.10.? ​​ origin, which consists of the compass points of singularity of the origin of the Cauchy fuss is called overtone(p) and provide be obtained from the amount for set(p) S.\nSolution of the Cauchy problem, which satisfies the Picard theorem is a fact result.\n exposition 2.11.? Solution, all(prenominal) point of which is dispirited singularity of the answer of the Cauchy problem pull up stakes be called e particular(a).\ngeometrically accompaniment settlement ascertain to fall curves that are non contained in t he ecumenical ascendent. on that pointfore, a special stem mess not live within the office D cosmos the total solution. It contribute not be obtained from the command solution rule in which no numerical determine ​​of C, including. It after part be obtained from the universal solution further when.\nThere are no special or uncomplete solutions. They cannister be obtained by gluing pieces of partial and special solutions.'