M-2
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ﺑﺴﻤﮫ ﺗﻌﺎﻟﯽ
رﺷﺘﮫ :ﻋﻤﺮان
ﺳﻮاﻻ ت اﻣﺘﺤﺎﻧﯽ :ﻣﻌﺎدﻻت دﯾﻔﺮاﻧﺴﯿﻞ ﻧﺎم و ﻧﺎم ﺧﺎﻧﻮادﮔﯽ : ﻧﯿﻢ ﺳﺎل :دوم
ﺳﺎﻋﺖ ﺷﺮوع١۴ : ﻣﺪت اﻣﺘﺤﺎن ١٢٠ :
٨۴- ٨۵
ﺳﺎل ﺗﺤﺼﯿﻠﯽ:
دﻗﯿﻘﮫ
ﺗﺎرﯾﺦ اﻣﺘﺤﺎن١٣٨۵/ ۴ / ٧ :
داﻧﺸﮕﺎه آزاد اﺳﻼﻣﯽ ﻣﺮﻧﺪ
ﺑﺎرم
(٣ﺟﻮاب ﻣﻌﺎدﻟﮫ دﯾﻔﺮاﻧﺴﯿﻞ زﯾﺮرا ﺑﺎ ﻣﻘﺪار اوﻟﯿﮫ داده ﺷﺪه ﺑﯿﺎﺑﯿﺪ.
y (π ) = 0, x > 0
2 cos x =y x x2
y′+
٢
(۴ﻣﺴﯿﺮھﺎی ﻗﺎﺋﻢ ﺑﺮ ﻣﻨﺤﻨﯽ ﺑﮫ ﻣﻌﺎدﻟﮫ زﯾﺮ را ﺑﺪ ﺳﺖ آورﯾﺪ.
+ y 2 =c2
2
) (x −c
٢
(۵ﻋﺎﻣﻞ اﻧﺘﮕﺮال ﺳﺎز ﻣﻌﺎدﻟﮫ دﯾﻔﺮاﻧﺴﯿﻞ زﯾﺮ را ﺑﺪﺳﺖ آورﯾﺪ.
)
(
e x ( x + 1) dx + ye y − xe x dy = 0
٢
ﺑﺎ آرزوی ﻣﻮﻓﻘﯿﺖ و ﮐﺎﻣﯿﺎﺑﯽ
ﻧﺎم و ﻧﺎم ﺧﺎﻧﻮادﮔﯽ اﺳﺘﺎد :اﺳﻤﺎﻋﯿﻞ ﻋﻠﯿﺰاده
اﻣﻀﺎء
ﺟﻤﻊ ﻧﻤﺮه
٢٠
رﺷﺘﮫ :ﻋﻤﺮان
ﺳﻮاﻻ ت اﻣﺘﺤﺎﻧﯽ :ﻣﻌﺎدﻻت دﯾﻔﺮاﻧﺴﯿﻞ ﻧﺎم و ﻧﺎم ﺧﺎﻧﻮادﮔﯽ : ﻧﯿﻢ ﺳﺎل :دوم
ﺳﺎﻋﺖ ﺷﺮوع١۴ : ﻣﺪت اﻣﺘﺤﺎن ١٢٠ :
٨۴- ٨۵
ﺳﺎل ﺗﺤﺼﯿﻠﯽ:
دﻗﯿﻘﮫ
ﺗﺎرﯾﺦ اﻣﺘﺤﺎن١٣٨۵/ ۴ / ٧ :
داﻧﺸﮕﺎه آزاد اﺳﻼﻣﯽ ﻣﺮﻧﺪ
ﺑﺎرم
(٣ﺟﻮاب ﻣﻌﺎدﻟﮫ دﯾﻔﺮاﻧﺴﯿﻞ زﯾﺮرا ﺑﺎ ﻣﻘﺪار اوﻟﯿﮫ داده ﺷﺪه ﺑﯿﺎﺑﯿﺪ.
y (π ) = 0, x > 0
2 cos x =y x x2
y′+
٢
(۴ﻣﺴﯿﺮھﺎی ﻗﺎﺋﻢ ﺑﺮ ﻣﻨﺤﻨﯽ ﺑﮫ ﻣﻌﺎدﻟﮫ زﯾﺮ را ﺑﺪ ﺳﺖ آورﯾﺪ.
+ y 2 =c2
2
) (x −c
٢
(۵ﻋﺎﻣﻞ اﻧﺘﮕﺮال ﺳﺎز ﻣﻌﺎدﻟﮫ دﯾﻔﺮاﻧﺴﯿﻞ زﯾﺮ را ﺑﺪﺳﺖ آورﯾﺪ.
)
(
e x ( x + 1) dx + ye y − xe x dy = 0
٢
ﺑﺎ آرزوی ﻣﻮﻓﻘﯿﺖ و ﮐﺎﻣﯿﺎﺑﯽ
ﻧﺎم و ﻧﺎم ﺧﺎﻧﻮادﮔﯽ اﺳﺘﺎد :اﺳﻤﺎﻋﯿﻞ ﻋﻠﯿﺰاده
اﻣﻀﺎء
ﺟﻤﻊ ﻧﻤﺮه
٢٠
