Question

$e^{\frac{dy}{dx}}=x+1$ given that when x = 0, y = 3, if x=1, then $y=\left(2\right).\ln \left(2\right)+k$, what is k?

• A. 1
• B. 2
• C. 4
• D. 5

Answer 1

The correct option is B 2

Given, $e^{\frac{dy}{dx}}=x+1$

$\Rightarrow \frac{dy}{dx}=\log (x+1)$
$\Rightarrow \int \frac{dy}{dx}dx=\int \log (x+1)dx$
$\Rightarrow y=-x+\log (x+1)+x\log (x+1)+c$
For $x=0;y=3\Rightarrow 3=c$
For $x=1;$$y=-1+\log 2+\log 2+3=2\log 2+\log 2$

$\therefore k=2$