Q241 / 270 · NDA 2017 (Phase 1) · Mathematics

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

  • Correct answer
    A
    $\mathrm{y}=\mathrm{xe}+\mathrm{c}$
  • B
    $\mathrm{y}=\mathrm{xe}+\mathrm{c}$
  • C
    $\mathrm{y}=\ln \mathrm{x}+\mathrm{c}$
  • D
    $\mathrm{x}=\ln \mathrm{y}+\mathrm{c}$

Solution

$\begin{aligned} & \ln \left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)-\mathrm{a}=0 \\ & \Rightarrow \ln \left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)=\mathrm{a} \\ & \Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{e}^{\mathrm{a}} \\ & \Rightarrow \int \mathrm{dy}=\int \mathrm{e}^{\mathrm{a}} \cdot \mathrm{dx} \\ & \Rightarrow \mathrm{y}=\mathrm{e}^{\mathrm{a}} \cdot \mathrm{x}+\mathrm{c}\end{aligned}$

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

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