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NDA 2017
Exam
NDA
Year
2017
Subject
Mathematics
Chapter
Differential Equations

NDA 2017 · Mathematics · Differential Equations

What is the solution of the differential equation ( dy dx )-a=0 ?

What is the solution of the differential equation \ln \left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)-\mathrm{a}=0 ?

Options

  1. Ay=xe+c\mathrm{y}=\mathrm{xe}+\mathrm{c}
  2. By=xe+c\mathrm{y}=\mathrm{xe}+\mathrm{c}
  3. Cy=ln⁡x+c\mathrm{y}=\ln \mathrm{x}+\mathrm{c}
  4. Dx=ln⁡y+c\mathrm{x}=\ln \mathrm{y}+\mathrm{c}

Correct answer

A. y=xe+c\mathrm{y}=\mathrm{xe}+\mathrm{c}

Step-by-step solution

ln⁡(dydx)−a=0⇒ln⁡(dydx)=a⇒dydx=\mathrmea⇒∫dy=∫\mathrmea⋅dx⇒y=\mathrmea⋅x+c\begin{aligned} & \ln \left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)-\mathrm{a}=0 \\ & \Rightarrow \ln \left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)=\mathrm{a} \\ & \Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=\mathrme^{\mathrm{a}} \\ & \Rightarrow \int \mathrm{dy}=\int \mathrme^{\mathrm{a}} \cdot \mathrm{dx} \\ & \Rightarrow \mathrm{y}=\mathrme^{\mathrm{a}} \cdot \mathrm{x}+\mathrm{c}\end{aligned}
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