If dy dx = y + 3 > 0 ;, ;y ( 0 ) = 2, then y ( 2 ) is equal to : - Vidyadip

MCQ

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

A
$5$
B
$13$
C
$-2$
✓
$7$

✓

Answer

Correct option: D.

$7$

d
$\frac{d y}{d x}=y+3$

$\Rightarrow \frac{1}{y+3} d y=d x$

$\Rightarrow \ln |(y+3)|=x+k,$ where $\mathrm{k}$ is a constant of

integration

$\Rightarrow(y+3)=c e^{x}$

Initially when $x=0, y=2$

$\Rightarrow c=5$

Finally the required solution is $y+3=5 c^{x}$

$\Rightarrow y(\ln 2)=5 c^{\ln 2}-3-10-3=7$

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