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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Differential Equations

NDA 2022 · Mathematics · Differential Equations

What does the equation x (d y)/(d x)-2 y=0 represent?

What does the equation xdydx−2y=0x \frac{d y}{d x}-2 y=0 represent?

Options

  1. AA family of straight lines
  2. BA family of circles
  3. CA family of parabolas
  4. DA family of ellipses

Correct answer

C. A family of parabolas

Step-by-step solution

xdydx−2y=0xdydx=2y\begin{aligned} & x \frac{d y}{d x}-2 y=0 \\ & x \frac{d y}{d x}=2 y\end{aligned}\int \frac{1}{\mathrm{y}} \mathrm{dy}=2 \int \frac{1}{\mathrm{x}} \mathrm{dx}ℓ ny =2ln⁡x+ℓncℓ ny =ℓnx2+ℓncℓny=ℓn(cx2)y=cx2\begin{aligned} & \ell \text{ ny }=2 \ln x+\ell \mathrm{nc} \\ & \ell \text{ ny }=\ell \mathrm{nx}^2+\ell \mathrm{nc} \\ & \ell \mathrm{n} y=\ell \mathrm{n}\left(\mathrm{cx}^2\right) \\ & \mathrm{y}=\mathrm{cx}^2\end{aligned}$ It represent the equation of parabolas.
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