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NDA 2015
Exam
NDA
Year
2015
Subject
Mathematics
Chapter
Differential Equations

NDA 2015 · Mathematics · Differential Equations

The order and degree of the differential equation of parabolas...

The order and degree of the differential equation of parabolas having vertex at the origin and focus at (a, 0) where a>0\mathrm{a} > 0, are respectively.

Options

  1. A1,1
  2. B2,1
  3. C1,2
  4. D2,2

Correct answer

A. 1,1

Step-by-step solution

The eq. of parabolas having vertex at (0,0) \ \text{ and } focus at (a,0)(a, 0), where (a>0)(a > 0) is : y2=4ax2y⋅dydx=4a\begin{aligned} & y^2=4 a x \\ & 2 y \cdot \frac{d y}{d x}=4 a \end{aligned} [on differentiating] On putting the value of (4a) in eq. (1) we get, 2x⋅dydx−y=0 in order =1  and  degree =1.\begin{gathered}2 \mathrm{x} \cdot \frac{\mathrm{dy}}{\mathrm{dx}}-\mathrm{y}=0 \\ \text{ in order }=1 \ \text{ and } \text{ degree }=1 .\end{gathered}
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