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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Differential Equations

NDA 2021 · Mathematics · Differential Equations

Which one of the following differential equations has the general...

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

Options

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

Correct answer

B. d2ydx2−y=0\frac{d^2 y}{d x^2}-y=0

Step-by-step solution

y=a⋅ex+b⋅e−xdydx=a⋅ex−b⋅e−x\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}d2ydx2=a⋅ex+b⋅e−x⇒d2ydx2=y∴d2ydx2−y=0\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}$
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