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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Differential Equations

NDA 2019 · Mathematics · Differential Equations

Which one of the following is the differential equation that...

Which one of the following is the differential equation that represents the family of curves y=12x2−cy=\frac{1}{2 x^2-c} where cc is an arbitrary constant?

Options

  1. Adydx=4xy2\frac{d y}{d x}=4 x y^2
  2. Bdydx=1y\frac{d y}{d x}=\frac{1}{y}
  3. Cdydx=x2y\frac{d y}{d x}=x^2 y
  4. Ddydx=−4xy2\frac{d y}{d x}=-4 x y^2

Correct answer

D. dydx=−4xy2\frac{d y}{d x}=-4 x y^2

Step-by-step solution

y=12x2−c⇒dydx=0−(4x)(2x2−c)2=−4x×1(2x2−c)2=−4x⋅y2⇒dydx=−4xy2\begin{aligned} & y=\frac{1}{2 x^2-c} \\ & \Rightarrow \frac{d y}{d x}=\frac{0-(4 x)}{\left(2 x^2-c\right)^2} \\ & =-4 x \times \frac{1}{\left(2 x^2-c\right)^2} \\ & =-4 x \cdot y^2 \\ & \Rightarrow \frac{d y}{d x}=-4 x y^2\end{aligned}
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