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Vector Algebra

Question
CBSEENMA12032978
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Form the differential equation of the family of parabolas having vertex at origin and axis along positive direction of x-axis.

Solution

Let P denote the family of given parabolas and let (a, 0) be the 'focus of a member of the given family, where a is an arbitrary constant. Therefore, equation of family P is
y2 = 4 a x    ...(1)
Differentiating both sides with respect to x, we get
2 straight y dy over dx space equals space 4 straight a       ...(2)

Substituting the value of 4 a from equation (2) in equation (1), we get
straight y squared space equals space open parentheses 2 straight y space dy over dx close parentheses space left parenthesis straight x right parenthesis space space space space or space space space straight y squared minus 2 xy dy over dx space equals space 0
which is the differential equation of the given family of parabolas.

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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