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Example 8 - Family of parabolas having vertex at origin - Formation of Differntial equation when general solution given

  1. Chapter 9 Class 12 Differential Equations
  2. Serial order wise
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Example 8 Form the differential equation representing the family of parabolas having vertex at origin and axis along positive direction of ๐‘ฅโˆ’๐‘Ž๐‘ฅ๐‘–๐‘ . Since parabola has axis along positive x-axis, its Equation : ๐‘ฆ๏ทฎ2๏ทฏ=4๐‘Ž๐‘ฅ Diff. w.r.t. ๐‘ฅ ๐‘‘๏ทฎ๐‘‘๐‘ฅ๏ทฏ ๐‘ฆ๏ทฎ2๏ทฏ๏ทฏ= ๐‘‘๏ทฎ๐‘‘๐‘ฅ๏ทฏ 4๐‘Ž๐‘ฅ๏ทฏ 2๐‘ฆ ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ฅ๏ทฏ=4๐‘Ž Putting Value of 4๐‘Ž in (1) ๐‘ฆ๏ทฎ2๏ทฏ=2๐‘ฆ ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ฅ๏ทฏ ร—๐‘ฅ ๐’š๏ทฎ๐Ÿ๏ทฏโˆ’๐Ÿ๐’™๐’š ๐’…๐’š๏ทฎ๐’…๐’™๏ทฏ = 0

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