Ex 9.3, 7

Transcript

Ex 9.3, 7 Form the differential equation of the family of Parabolas having vertex at origin and 𝑎𝑥𝑖𝑠 along positive 𝑦−𝑎𝑥𝑖𝑠 Equation Of Parabola where vertex is at origin and axis along y-axis is 𝑥﷮2﷯=4𝑎𝑦 Differentiating Both Sides w.r.t. 𝑥 2𝑥=4𝑎 𝑑𝑦﷮𝑑𝑥﷯ 𝑥=2𝑎 𝑑𝑦﷮𝑑𝑥﷯ 𝑥=2𝑎 𝑦﷮′﷯ Dividing (2) by (1) i.e. (2) ÷ (1) 𝑥﷮ 𝑥﷮2﷯﷯= 2𝑎 𝑦﷮′﷯﷮4𝑎𝑦﷯ 1﷮𝑥﷯= 𝑦﷮′﷯﷮2𝑦﷯ 2𝑦=𝑥 𝑦﷮′﷯ ∴ 𝒙 𝒚﷮′﷯−𝟐𝒚=𝟎 is the required differential equation