Question

If $\frac{dy}{dx}=y+3$ and $y\left(0\right)=2,$ then $y\left(\ln 2\right)$ is/are equal to:

• A. $5$
• B. $-13$
• C. $-7$
• D. $7$

Answer 1

Answer: (B), (D)

$7$

$\frac{dy}{dx}=y+3$
$\Rightarrow \int \frac{dy}{y+3}=\int dx$
$\Rightarrow \ln |y+3|=x+c\cdots \left(i\right)$
Since, $y\left(0\right)=2$
$\Rightarrow \ln 5=c$
Now, from $\left(i\right)$
$\ln |y+3|=x+\ln 5$

When $x=\ln 2,$ then
$\ln |y+3|=\ln 2+\ln 5$
$\Rightarrow \ln |y+3|=\ln 10$
$\Rightarrow y+3=\pm 10\Rightarrow y=7,-13$