Q248 / 270 · NDA 2021 (Phase 1) · Mathematics

Which one of the following differential equations has the general solution $y=a e^x+b e^{-x}$ ?

  • A
    $\frac{d^2 y}{d x^2}+y=0$
  • Correct answer
    B
    $\frac{d^2 y}{d x^2}-y=0$
  • C
    $\frac{d^2 y}{d x^2}+y=1$
  • D
    $\frac{d y}{d x}-y=0$

Solution

$\begin{aligned} & y=a \cdot e^x+b \cdot e^{-x} \\ & \frac{d y}{d x}=a \cdot e^x-b \cdot e^{-x}\end{aligned}$ $\begin{aligned} & \frac{d^2 y}{d x^2}=a \cdot e^x+b \cdot e^{-x} \Rightarrow \frac{d^2 y}{d x^2}=y \\ & \therefore \frac{d^2 y}{d x^2}-y=0\end{aligned}$

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

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