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If $\frac{d y}{d x}=y+3>0$ and $y(0)=2$, then $y(\ln 2)$ is equal to
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The correct answer is:
7
7
$\frac{d y}{d x}=y+3 \Rightarrow \frac{d y}{y+3}=d x$
$\ln (y+3)=x+c$
$x=0 \Rightarrow y=2$
$\Rightarrow \ln 5=0+c$
$c=\ln 5$
$\ln (y+3)=x+\ln 5$
$y+3=e^{x+\ln 5} \Rightarrow y+3=e^{\ln 2+\ln 5}$
$y+3=10 \Rightarrow y=7$
$\ln (y+3)=x+c$
$x=0 \Rightarrow y=2$
$\Rightarrow \ln 5=0+c$
$c=\ln 5$
$\ln (y+3)=x+\ln 5$
$y+3=e^{x+\ln 5} \Rightarrow y+3=e^{\ln 2+\ln 5}$
$y+3=10 \Rightarrow y=7$
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