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NDA 2020
Exam
NDA
Year
2020
Subject
Mathematics
Chapter
Differential Equations

NDA 2020 · Mathematics · Differential Equations

What is the solution of the differential equation ((d y)/(d x))=x ?

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

Options

  1. Ay=ex+cy=e^x+c
  2. By=e−x+cy=e^{-x}+c
  3. Cy=ln⁡x+cy=\ln x+c
  4. Dy=2ln⁡x+cy=2 \ln x+c

Correct answer

A. y=ex+cy=e^x+c

Step-by-step solution

ln⁡(dydx)=xdydx=ex\begin{aligned} & \ln \left(\frac{d y}{d x}\right)=x \\ & \frac{d y}{d x}=e^x \end{aligned} Integrating both sides, we get ∫dy=∫ex⋅dxy=ex+C\int d y=\int e^x \cdot d xy=e^x+C, where C=C= integration constant.
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