Q234 / 270 · NDA 2020 · Mathematics

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

  • Correct answer
    A
    $y=e^x+c$
  • B
    $y=e^{-x}+c$
  • C
    $y=\ln x+c$
  • D
    $y=2 \ln x+c$

Solution

$\begin{aligned} & \text { } \ln \left(\frac{d y}{d x}\right)=x \\ & \frac{d y}{d x}=e^x \end{aligned}$ Integrating both sides, we get $\int d y=\int e^x \cdot d x$ $y=e^x+C$, where $C=$ integration constant.

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

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