Question

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

• A. 7
• B. 5
• C. 13
• D. -2

Answer 1

Answer: (A)

7

$\frac{dy}{dx}=y+3$
$\Rightarrow \frac{dy}{y+3}=dx$
On integrating
$\ln |y+3|=x+c$
$\therefore \ln (y+3)=x+c$
Since $y\left(0\right)=2$
$\therefore c=\ln 5$
$\Rightarrow \ln (y+3)=x+\ln 5$
Substitute $x=\ln 2$
$\Rightarrow yln2=7$.
Hence, option 'A' is correct.