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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Differential Equations

NDA 2023 · Mathematics · Differential Equations

What is the differential equation of all parabolas of the type...

What is the differential equation of all parabolas of the type y2=4a(x−b)y^2=4 a(x-b) ?

Options

  1. Ad2ydx2+(dydx)2=0\frac{d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^2=0
  2. Bd2ydx2+x2(dydx)2=0\frac{d^2 y}{d x^2}+x^2\left(\frac{d y}{d x}\right)^2=0
  3. Cy2d2ydx2+(dydx)2=0y^2 \frac{d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^2=0
  4. Dyd2ydx2+(dydx)2=0y \frac{d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^2=0

Correct answer

D. yd2ydx2+(dydx)2=0y \frac{d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^2=0

Step-by-step solution

Since, y2=4ax−4ab⇒2ydydx=4a⇒yd2ydx2+y^2=4 a x-4 a b\Rightarrow 2 y \frac{d y}{d x}=4 a \Rightarrow y \frac{d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^2=0
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