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Vector Algebra

Question
CBSEENMA12032969
Wired Faculty App

Form the differential equation of the family of circles having centre on x-axis and radius 3 units.

Solution

The equation of the family of circles having centre (0, b) on y-axis and radius 3 units is
x2 + (y – b)2 = 9    ...( 1)
Differentiating both sides w.r.t x, we get,
               2 straight x plus 2 left parenthesis straight y minus straight b right parenthesis dy over dx space equals space 0 space space space or space space space straight y space minus space straight b space equals space minus fraction numerator straight x over denominator begin display style dy over dx end style end fraction
Putting this value of y - b in (1), we get,
                        straight x squared plus straight x squared over open parentheses begin display style dy over dx end style close parentheses squared space equals space 9    or     open parentheses straight x squared minus 9 close parentheses plus straight x squared over open parentheses begin display style dy over dx end style close parentheses squared space equals 0
or                   left parenthesis straight x squared minus 9 right parenthesis space open parentheses dy over dx close parentheses squared plus straight x squared space equals space 0
which is 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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