Q37 / 90 · JEE Main 2011 · Mathematics

If $\frac{d y}{d x}=y+3>0$ and $y(0)=2$, then $y(\ln 2)$ is equal to

  • A
    5
  • B
    13
  • C
    -2
  • Correct answer
    D
    7

Solution

$\frac{d y}{d x}=y+3 \Rightarrow \frac{d y}{y+3}=d x$ $\ln (y+3)=x+c$ $x=0 \Rightarrow y=2$ $\Rightarrow \ln 5=0+c$ $c=\ln 5$ $\ln (y+3)=x+\ln 5$ $y+3=e^{x+\ln 5} \Rightarrow y+3=e^{\ln 2+\ln 5}$ $y+3=10 \Rightarrow y=7$

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

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