Анықтама 8.
у'+p(x)y=q(x) (9)
түріндегі теңдеуді бірінші ретті сызықтық дифференциалдық теңдеу деп атайды.
Мұнда р(х),g(х) үздіксіз функциялар.
Байқасаңдар, у' туындысы функция у-тің сызықтық функциясы. Сондықтан да сызықтық теңдеу деп аталған.
Егер g(x) 0 -са, онда (9) теңдеу айнымалысы ажыратылатын теңдеуге айналады. Жалпы жағдайда (9) теңдеудің айнымалысы ажыратылмайды.
Сондықтан (9) теңдеудің өзіне тән шығару әдісін көрсетеміз. Ол үшін белгісіз функцияны у=uv (*) түрінде іздейміз, мұнда u(x) және v(x) дифференциялданатын функциялар.Туындыны табамыз.
у'=u'v+uv'
Енді осы өрнектерді (9) теңдеуге қойып, оны мына түрге келтіруге болады.
u'v+u(v'+p(x))=q(x) (10)
v-функциясын v'+p(x)v өрнегін x-ке қарағанда тепе–теңдікке айландыратындай етіп таңдап аламыз. Ондай функция
v'+p(x)v=0 (11)
теңдеудің шешімі бола алады.
(11)- теңдеудің бір ғана шешімін табу жеткілікті .
Мысалға, ондай шешім:
(12)
болады.
Ал у=uv функциясы (10) теңдеудің шешімі болу үшін u-функциясы u'v0(x)=q(x) немесе
(13)
теңдеуінің шешімі болуға тиіс. (1.18) теңдеуді шешеміз
![](data:image/png;base64,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)
Енді v және u фунцияларының өрнегін (*) теңдікке апарып қойсақ,
(14)
іздеп отырған шешімді табамыз. (1.19)-формуланы мына түрде де
(15)
жазуға болады.
Бірақ бұл жағдайда формулаға кіретін әрбір анықталмаған интегралды бір ғана алғашқы функция ретінде қарастырған жөн болады.
(14) немесе (15) формулаларын осылай қорыту әдісін Бернулли әдісі деп атайды.
Сөйтіп сызықтық теңдеуді шешу ( шығару) үшін қорытылған (14) немесе (15) формулаларын пайдалануға болады. Алайда Бернулли әдісін әрбір теңдеуге тікелей қолдану арқылы да шешеді.
Бернулли әдісін көрсету барысында байқағанымыздай сызықтық теңдеудің шешімін табу төмендегі дифференциалды теңдеулер системасына келіп тіреледі.
(16)
Системаны құрайтын теңдеулердің екеуі де айнымалысы ажыратылатын теңдеулер. Біріншісін шешіп v функциясын табамыз. Табылған функцияны екіншісіне қойып u функциясын анықтаймыз. Соңында
y=u·v
түріндегі берілген сызықтық теңдеуінің шешімі табылады.
Достарыңызбен бөлісу: |