Q5 of 26 Page 1

Find the differential equation representing the family of curves v = where A and B are arbitrary constants.

To get the differential equation form an algebraic equations we need to remove the arbitrary constants by differentiating equation.


As, v =


We need to remove both parameters A and B to get the differential equation.


Differentiating w.r.t to r ,we get-



∵


∴


⇒


Again differentiating w.r.t r. Applying product rule of differentiation to evaluate LHS of equation.


∴


⇒


⇒ is the required differential equation.


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