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CBSE Class 12-science Answered

obtain the  differential equation of the family of circles passing through the point (a,0) and (-a,0)
Asked by ppratim02 | 16 Nov, 2016, 05:01: PM
answered-by-expert Expert Answer
begin mathsize 18px style Since space the space circles space pass space through space the space points space left parenthesis straight a comma 0 right parenthesis space and space left parenthesis negative straight a comma 0 right parenthesis comma space the space centre space of space the space circle space will space be space the space origin space and space the space circle space will space have space radius space equals space straight a So comma space the space general space equation space of space such space straight a space circle space is space open parentheses straight x minus straight a close parentheses squared plus straight y squared equals straight a squared space..... left parenthesis straight i right parenthesis The space equation space should space be space differentiated space once space since space there space is space only space one space arbitrary space constant comma space straight a. Differentiating space left parenthesis straight i right parenthesis space on space both space sides comma space we space get 2 left parenthesis straight x minus straight a right parenthesis plus 2 straight y dy over dx equals 0 space..... left parenthesis ii right parenthesis rightwards double arrow straight x minus straight a equals negative straight y dy over dx space space and space space straight a equals straight x plus straight y dy over dx Substituting space the space values space of space straight x minus straight a space and space straight a space in space left parenthesis straight i right parenthesis comma space we space get open parentheses straight y dy over dx close parentheses squared plus straight y squared equals open parentheses straight x plus straight y dy over dx close parentheses squared space rightwards double arrow straight y squared open parentheses dy over dx close parentheses squared plus straight y squared equals straight x squared plus 2 xy dy over dx plus straight y squared open parentheses dy over dx close parentheses squared rightwards double arrow straight y squared equals straight x squared plus 2 xy dy over dx which space is space the space required space differential space equation. end style
Answered by Rebecca Fernandes | 17 Nov, 2016, 09:08: AM

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CBSE 12-science - Maths
the question is given in the attachment in case the attachment is not appearing i have mentioned this question: Solve the differential equation yexydx=⎛⎜⎝xexy+y2⎞⎟⎠ dy. (toppr.com) in this question they have solved the differential equation by substituting v = x/y, but as of my knowledge, this substitution can be made only for zero order homogeneous differential equations, yet the answer they got is correct and is verified by calculator, so does this mean that we can appl this substitution to any differential equation? PS: in some sites they have solved this question by other methods and they have specified substituting v = x/y wont work here as this is not a homogenous differential equation. So can you clarify what is the correct way to solve this question, THANK YOU!
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Asked by ashwinskrishna2006 | 24 Dec, 2023, 04:59: PM
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CBSE 12-science - Maths
Please refer to the uploaded image for the doubt.
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Asked by arjunsah797 | 22 May, 2022, 10:25: AM
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CBSE 12-science - Maths
sir i only need the correct option
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CBSE 12-science - Maths
1st ques with explanation 
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CBSE 12-science - Maths
11th sum plz
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CBSE 12-science - Maths
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Asked by lovemaan5500 | 20 Aug, 2019, 05:10: PM
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CBSE 12-science - Maths
Define differential equation.
Asked by Topperlearning User | 08 Oct, 2014, 01:42: PM
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CBSE 12-science - Maths
Define the order of a differential equation.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
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CBSE 12-science - Maths
Find the order and degree of the differential equation: .
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
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CBSE 12-science - Maths
Find the order and degree of the differential equation: .
Asked by Topperlearning User | 04 Nov, 2016, 07:15: AM
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