The solution of the equation dy dx = y( e^x + 1) is - Vidyadip

MCQ

The solution of the equation $\frac{{dy}}{{dx}} = y({e^x} + 1)$ is

A
$y + {e^{({e^x} + x + c)}} = 0$
✓
$\log y = {e^x} + x + c$
C
$\log y + {e^x} = x + c$
D
None of these

✓

Answer

Correct option: B.

$\log y = {e^x} + x + c$

b
(b) $\frac{{dy}}{{dx}} = y({e^x} + 1)$ ==> $\frac{{dy}}{y} = ({e^x} + 1)dx$

Integrating both sides, we get $\log y = {e^x} + x + c$.

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