Ex 9.3, 7 - Family of Parabolas having vertex at origin, axis - Formation of Differntial equation when general solution given

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  1. Chapter 9 Class 12 Differential Equations
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Ex 9.3, 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๏ทฎ2๏ทฏ=4๐‘Ž๐‘ฆ Differentiating Both Sides w.r.t. ๐‘ฅ 2๐‘ฅ=4๐‘Ž ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ฅ๏ทฏ ๐‘ฅ=2๐‘Ž ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ฅ๏ทฏ ๐‘ฅ=2๐‘Ž ๐‘ฆ๏ทฎโ€ฒ๏ทฏ Dividing (2) by (1) i.e. (2) รท (1) ๐‘ฅ๏ทฎ ๐‘ฅ๏ทฎ2๏ทฏ๏ทฏ= 2๐‘Ž ๐‘ฆ๏ทฎโ€ฒ๏ทฏ๏ทฎ4๐‘Ž๐‘ฆ๏ทฏ 1๏ทฎ๐‘ฅ๏ทฏ= ๐‘ฆ๏ทฎโ€ฒ๏ทฏ๏ทฎ2๐‘ฆ๏ทฏ 2๐‘ฆ=๐‘ฅ ๐‘ฆ๏ทฎโ€ฒ๏ทฏ โˆด ๐’™ ๐’š๏ทฎโ€ฒ๏ทฏโˆ’๐Ÿ๐’š=๐ŸŽ is the required differential equation

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