Ex 9.3, 7 - Family of Parabolas having vertex at origin, axis

Ex 9.3, 7 - Chapter 9 Class 12 Differential Equations - Part 2


Question 7 Form the differential equation of the family of Parabolas having vertex at origin and ๐‘Ž๐‘ฅ๐‘–๐‘  along positive ๐‘ฆโˆ’๐‘Ž๐‘ฅ๐‘–๐‘  Equation Of Parabola where vertex is at origin and axis along y-axis is ๐‘ฅ^2=4๐‘Ž๐‘ฆ Differentiating Both Sides w.r.t. ๐‘ฅ 2๐‘ฅ=4๐‘Ž ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ ๐‘ฅ=2๐‘Ž ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ ๐‘ฅ=2๐‘Ž๐‘ฆ^โ€ฒ Dividing (2) by (1) i.e. (2) รท (1) ๐‘ฅ/๐‘ฅ^2 =(2๐‘Ž๐‘ฆ^โ€ฒ)/4๐‘Ž๐‘ฆ 1/๐‘ฅ=๐‘ฆ^โ€ฒ/2๐‘ฆ 2๐‘ฆ=๐‘ฅ๐‘ฆ^โ€ฒ โˆด ๐’™๐’š^โ€ฒโˆ’๐Ÿ๐’š=๐ŸŽ is the required differential equation

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.