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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Differential Equations

NDA 2013 · Mathematics · Differential Equations

The differential equation of the curve y= x is

The differential equation of the curve y=sin⁡xy=\sin x is

Options

  1. Ad2ydx2+ydydx+x=0\frac{d^2 y}{d x^2}+y \frac{d y}{d x}+x=0
  2. Bd2ydx2+y=0\frac{d^2 y}{d x^2}+y=0
  3. Cd2ydx2−y=0\frac{d^2 y}{d x^2}-y=0
  4. Dd2ydx2+x=0\frac{d^2 y}{d x^2}+x=0

Correct answer

B. d2ydx2+y=0\frac{d^2 y}{d x^2}+y=0

Step-by-step solution

y=sin⁡xdydx=cos⁡xd2ydx2=−sin⁡x\begin{aligned} & y=\sin x \\ & \frac{d y}{d x}=\cos x \quad \frac{d^2 y}{d x^2}=-\sin x\end{aligned}\therefore \quad y+\frac{d^2 y}{d x^2}=0\frac{d y}{d x}=\frac{1}{x+y+1}$
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