Q184 / 270 · NDA 2010 (Phase 2) · Mathematics

What is the general solution of $\left(1+x^x\right) y d y=e^x d x ?$

  • Correct answer
    A
    $y^2=\ln \left[c^2\left(e^x+1\right)\right]^2$
  • B
    $y=\ln \left[c\left(e^x+1\right)\right]$
  • C
    $y^2=\ln \left[c\left(e^x+1\right)\right]$
  • D
    None of the above where $c$ is a constant of integration.

Solution

$\begin{aligned} & y d y=\int \frac{e^x}{e^{x+1}} d x \\ & \therefore \frac{y^2}{2}=\log \left(e^x+1\right)+\log c \\ & y^2=2 \log \left(e^x+1\right)+2 \log c \\ & y^2=\log \left(e^x+1\right)^2 c^2\end{aligned}$

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

Relevant Questions