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

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

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Transcript

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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