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CBSE Class 12 · 2011 · Differential EquationsLong Answer

Form the differential equation of the family of parabolas having vertex at the origin and axis along the positive

y

-axis.

Answer: $x \frac{d y}{d x} - 2 y = 0$

Solution

Such parabolas are

x^{2} = 4 a y

(one parameter

a

). Differentiate:

2 x = 4 a \frac{d y}{d x} \Rightarrow a = \frac{x}{2 y ^{'}}

Substitute into

x^{2} = 4 a y

:

x^{2} = 4 \cdot \frac{x}{2 y ^{'}} \cdot y \Rightarrow x y^{'} = 2 y

x \frac{d y}{d x} - 2 y = 0

CBSE Class 12 Board · 2011 · Subjective

Practise more: all CBSE board PYQs on Differential Equations →

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