Q246 / 270 · NDA 2021 (Phase 1) · Mathematics

If the general solution of a differential equation is $y^2+2 c y-c x+c^2=0$, where $c$ is an arbitrary constant, then what is the order of the differential equation?

  • A
    $1$
  • Correct answer
    B
    $2$
  • C
    $3$
  • D
    $4$

Solution

$y^2+2 c y-c x+c^2=0$ $\begin{aligned} & 2 y \cdot \frac{d y}{d x}+2 c \cdot \frac{d y}{d x}-c=0 \\ & 2\left(\frac{d y}{d x}\right)^2+2 y \cdot \frac{d^2 y}{d x^2}+2 c \cdot \frac{d^2 y}{d x^2}=0\end{aligned}$ $(y+c) \cdot \frac{d^2 y}{d x^2}+2 \frac{d y}{d x}$

Hence, the correct answer is option: 'B'.

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