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259091500 - משוואות דיפ' חלקיות - מרוכז

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נתונה הבעיה

u subscript t t end subscript equals a squared u subscript x x end subscript comma space 0 less or equal than x less or equal than L comma space 0 less than t less than infinity u left parenthesis 0 comma t right parenthesis equals u left parenthesis L comma t right parenthesis equals 0 u left parenthesis x comma 0 right parenthesis equals sum from n equals 1 to N of B subscript n sin left parenthesis fraction numerator n straight pi straight x over denominator L end fraction right parenthesis comma u subscript t left parenthesis x comma 0 right parenthesis equals sum from n equals 1 to N of A subscript n sin left parenthesis fraction numerator n straight pi straight x over denominator L end fraction right parenthesis

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נתונה הבעיה

u subscript t t end subscript minus u subscript x x end subscript equals 0 space space space space space space space space space space space minus infinity less than x less than infinity comma space space space space minus infinity less than t less than infinity u left parenthesis x comma 0 right parenthesis equals sin left parenthesis x right parenthesis space space space space space space space space space space space space space minus infinity less than x less than infinity u subscript t left parenthesis x comma 0 right parenthesis equals fraction numerator 1 over denominator 1 plus x squared end fraction space space space space space space space minus infinity less than x less than infinity

הגל המתקדם שמאלה (גל נסוג) הוא: 

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נתונה הבעיה

u subscript t t end subscript minus u subscript x x end subscript equals 0 comma space space space space space space space space 0 less than x less than pi comma space space t greater than 0 u left parenthesis 0 comma t right parenthesis equals 0 comma space space space space space space space space space space space t greater or equal than 0 u left parenthesis pi comma t right parenthesis equals 0 comma space space space space space space space space space space t greater or equal than 0 u left parenthesis x comma 0 right parenthesis equals x comma space space space space space space space space space space 0 less or equal than x less or equal than pi u subscript t left parenthesis x comma 0 right parenthesis equals 0 comma space space space space space space space space 0 less or equal than x less or equal than pi

ונתון הפתרון למד"ח ותנאי השפה:  u left parenthesis x comma t right parenthesis equals sum from n equals 1 to infinity of open parentheses A subscript n cos left parenthesis n t right parenthesis plus B subscript n sin left parenthesis n t right parenthesis close parentheses sin left parenthesis n x right parenthesis

הפתרון לבעיה  הוא: 

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u subscript t t end subscript minus u subscript x x end subscript equals 0 space space space space space minus infinity less than x less than infinity comma space space minus infinity less than t less than infinity u left parenthesis x comma 0 right parenthesis equals vertical line x vertical line space space space space space space space minus infinity less than x less than infinity u subscript t left parenthesis x comma 0 right parenthesis equals 4 x space space space space space space space minus infinity less than x less than infinity

הערך של u left parenthesis 1 comma 2 right parenthesis  הוא

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נתונה הבעיה

u subscript t t end subscript minus u subscript x x end subscript equals 0 space space space space space space space space space space space 0 less than x less than infinity comma space space minus infinity less than t less than infinity u left parenthesis x comma 0 right parenthesis equals 0 space space space space space space space space space space space space space 0 less than x less than infinity u subscript t left parenthesis x comma 0 right parenthesis equals 2 x space space space space space space space space space space 0 less than x less than infinity u subscript x left parenthesis 0 comma t right parenthesis equals 0 space space space space space space space space space space space 0 less than x less than infinity

הערך של u left parenthesis 1 comma 1 right parenthesis שווה

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