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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Differential Equations

NDA 2021 · Mathematics · Differential Equations

What is the solution of the following differential equation? ((d...

What is the solution of the following differential equation? \ln \left(\frac{d y}{d x}\right)+y=x

Options

  1. Aex+ey=ce^x+e^y=c
  2. Bex+y=ce^{x+y}=c
  3. Cex−ey=ce^x-e^y=c
  4. Dex−y=ce^{x-y}=c

Correct answer

C. ex−ey=ce^x-e^y=c

Step-by-step solution

ln⁡(dydx)=x−y\ln \left(\frac{d y}{d x}\right)=x-yex−y=dydxex⋅dx=ey⋅dy\begin{aligned} & e^{x-y}=\frac{d y}{d x} \\ & e^x \cdot d x=e^y \cdot d y\end{aligned}On integrating both sides, we get, $\int e^x \cdot d x=\int e^y \cdot d y\begin{aligned} & e^x=e^y+c \\ & e^x-e^y=c\end{aligned}$$$
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