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Vector Algebra

Question
CBSEENMA12032979
Wired Faculty App

Form the differential equation of the family of parabolas having vertex at origin and axis along positive direction of y-axis.

Solution

Let P denote the family of parabolas and let S (0. a) be the focus of a member of the given family, where a is an arbitrary constant.
∴    equation of family P is
a2 = 4 a y    ...(1)
Differentiating both sides w.r.t. x, we get.
                           2 straight x space equals space 4 straight a dy over dx
therefore space space space space 4 straight a space equals space fraction numerator 2 straight x over denominator begin display style dy over dx end style end fraction
Putting value of 4a in (1), we get,
                            straight x squared space equals space fraction numerator 2 straight x over denominator begin display style dy over dx end style end fraction straight y space space space or space space space space straight x dy over dx space equals space 2 straight y
which is the required differential equation. 


Some More Questions From Vector Algebra Chapter

Determine order and degree (if defined) of differential equations:
y' + y = ex

Determine order and degree (if defined) of differential equations:
y'' + (y')2 + 2 y = 0

Determine order and degree (if defined) of differential equations:
y″ + 2y′ + sin y = 0

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